I don't at all doubt your responsibility, that is obvious. Unfortunately, bringing a parrot into your family, regardless of the species, absolutely must be the decision of every person in your home, not just you or your siblings. The issue is that parrots are extremely intelligent, all of them, regardless of their size, they possess the intelligence of a 3-4 year-old human child. As such, if they aren't cared for in very much the way you care for a child, they end-up developing self-mutilation conditions and feather-destructive behaviors due to boredom, a lack of stimulation, and a feeling of being left-out of the "flock"....
From the sounds of it, you'd be planning on keeping your parrot in your bedroom, correct? This is a very bad idea, and typically is not fair to any parrot. Parrots should have their main-cages located in the "main room" of your home, or the room where the people who live in the home spend most of their time when they are at home. If your bird's main-cage is going to be required to be kept in your bedroom, that means that when you're not home, the bird is going to have to be locked inside it's cage, by itself, listening to people at home, knowing that their "flock" is home, but that they are not included....Forgetting that any species of parrot requires an absolute minimum of at least 5 hours each day out-of-cage-time, more is better, they also need to be among their "flock", as after-all, they are "flock" animals. And even if they aren't being directly interacted with, having their cage located in the room where the people who live in the house watch TV, read, eat meals, talk, where visitors spend time when they come over, etc., brings them a feeling of comfort, contentment, and typically this is when they are best at entertaining themselves inside of their cages (assuming that you'll be able to keep between 6-10 different types of toys inside the cage at all times, and rotate new ones in each month to prevent boredom)...It's quite common for a bird locked inside a cage is kept in a back bedroom, and they can hear that people are home in the house but that they aren't included, that this is when the constant screaming and squawking starts, along with the feather-destructive behavior.
And as far as their life-spans, it doesn't sound like you quite understand how long a properly cared-for Budgie or Cockatiel will live. You're now 13, so you only 4-5 years until you start college, but you made a statement of "If the bird is healthy and survives that long..."...The fact is that the average lifespan of an American Budgie that is on a healthy, low-fat, varied diet and who is given adequate attention and love is between 15-20 years, with the record for the oldest American Budgies age being 29. And Cockatiels on-average are about 5 years or so longer than that of a Budgie...Unfortunately a lot of people think that a Budgie and/or a Cockatiel will only live to be 5-6 years old, and the only reason that this happens is because they aren't well-cared for, usually fed an all-seed diet that causes Fatty Liver Disease, and they aren't given nearly enough attention or out-of-cage-time each day. There should be NO DIFFERENCE between the way you care for a Budgie or Cockatiel and the way you would care for a Conure, a Pionus, an Amazon, or a Macaw. Budgies and Cockatiels are extremely intelligent, much more so than any dog, and as such they become very bored very quickly.
My concern here is what happens when you do start college? Who is going to allow your bird to get at least 5-6 hours each day of out-of-cage time? Who is going to make sure that your bird is not just being fed seeds and pellets, but also fresh veggies every single day? And forgetting college for the moment, you're now only 13 years old....There is a huge difference between the social life of a 13 year-old and a 16 year-old, and then again between that of a 16 year-old and an 18 year-old...and there should be! You are going to need to live your life, and there is no shame in that! This is why it's so very difficult for teenagers and young adults who have human children, they either essentially give-up their teenage and young-adult years to be responsible parents, or they don't, and their child suffers for it, or ends-up being raised by their parents/relatives. And though a parrot is not a human child, it's also not a dog, a cat, a guinea pig, a reptile, etc. You wouldn't lock a dog inside of a cage for 7-8 hours a day in your bedroom, so why would you do that with a parrot who has the intelligence of a 3-4 year-old child? That's the way you need to start thinking about this decision...
***As far as the financial part of this decision goes, I understand you bring-in some money from the pet-sitting...However, I have 2 questions about the pet-sitting gig....Firstly, how much of your time is taken-up by the pet-sitting and would be taken-away from being with your own parrot, and then secondly, do you bring-in enough money to not only buy food for your bird every month, but to pay for Avian Vet care? This is something that a lot of kids/teenagers who have pet birds, reptiles, etc. get into and have a huge issue with, because even though their parents allow them to buy the pet and bring the pet into the home, the parents rarely agree to pay for the very expensive specialty Vet care that exotic-pets require. You absolutely cannot take a parrot to either a General Vet or an "Exotic's Vet" who treats ALL species of animals, as they usually end-up doing much more harm than good. You must find either a Certified Avian Vet (CAV) or an Avian Specialist Vet who only treats birds and who has extra education, training, and experience doing so. Exotic's Vets typically do not have any special training or education in treating birds at all.
So figure that buying your parrot a high-quality pellet, high-quality and low-fat seed-mix, and then fresh veggies/fruit will cost you around $40 a month, give or take. You should not ever just buy cheap parrot seed at a grocery store or Walmart, they should eat a daily staple of a high-quality, Natural pellet (no fruit pellets), along with a low-fat, varied seed-mix as a supplement which contains no sunflower seeds, no nuts/peanuts, and no corn. And then they need fresh veggies every day, and fresh fruit 4-5 times a week as a treat...The pellets and the seed is obviously the bulk of the cost.
***However, what people don't ever think about or plan for is specialty Avian Vet care. Your bird should see either a CAV or an Avian Specialist Vet at least once every year for a "Wellness Exam" which includes routine blood-work and fecal cultures, and a plain-film x-ray is also a good idea. But figure the basic Wellness-Exam with routine, baseline blood-work and fecal cultures will cost you around $200. However, whenever your parrot becomes ill, this is where there is usually a problem...All birds possess a natural, innate survival instinct where they hide all outward signs of illness/pain for as long as they possibly can. This protects them and their flock-members from being the target of predators. So by the time we as people see visible, outward signs that our birds are sick or in pain/injured, they've usually been sick for weeks, if not months, and getting them to a CAV or Avian Specialist immediately is not optional, as little time is left, even for something as simple as a Bacterial or Fungal Infection, as by the time we know they have one, they can be close to Sepsis/Systemic Infection and death. This is where young people/teenagers typically have to go to their parents and beg them to take the bird to the CAV, because they don't have the hundreds to thousands of dollars this costs. My Green Cheek Conure recently developed an infection that started in his toenail and had spread to his foot by the time I was aware of it. And this was the result of a simple toenail-clipping, where one of his toenails bled and bacteria entered into his toenail. Such a freak, simple thing almost killed him, as by the time I was aware that there was a problem, the infection had almost spread to his bloodstream. He had to have blood-work, a culture/sensitivity and microscopy of a swab taken from his toe/foot tissue, and a plain-film x-ray to diagnose that it was an infection, what type of infection it was, what specific microbe was causing the infection, and what specific Antibiotic would treat the bacteria that was causing it, and to make sure that the infection had not spread into the bones of his foot/leg, which would have most-likely required amputation to save his life. Luckily it hadn't, and we were able to clear-up the infection with antibiotic injections and oral antibiotics. So the office-visit/exam with my CAV, all of the lab tests and the x-ray, and the medications cost me just under $1,000. And had he needed surgery, the total cost would have been easily between $2,000-$3,000...So the question you need to ask yourself is whether or not you'll have that kind of money on-the-spot, at any moment, if your bird becomes sick or injured, and if not, will your parents be willing/able to pay for it? If not, then it's not a good idea to bring home a bird...
You just need to carefully examine these questions/situations that can occur, and decide whether or not you're going to be able to provide the proper time, care, attention, and financial needs that any species of parrot requires. If you're not sure, and your parents are not on-board and willing to help you, then it's probably not a good idea...
