As someone who has been in a very similar situation, I can tell you that it just isn't easy, nor is it going to get any easier, lol. I'd rather be blunt than lie to you. I had an apartment during undergrad where I had my Budgie, and for whatever reason I decided to get an Australian Cattle Dog puppy my Junior year of undergrad (stupid, let's get the breed of dog that needs to run all day long, every single day), and that was difficult at best. My Budgies at the time I moved him from my mom's house was about 13 years old and had always been surrounded by multiple people, even though he was bonded with me, and he displayed much the same behavior as your Caique is. It's just the change of going from being around multiple people and then suddenly being alone all day by themselves, so when you get home he's so excited that you're finally there that he can't stand not having you directly interacting with him all the time...And when other people come over to your apartment now, it's very much like how it was at your parent's house again, multiple people at home doing their own thing, and he feels comfortable and secure in that type of situation, thus he's very content to entertain himself...But as soon as it's just you and him again, it's different again, and he wants direct attention...It's a big change for him and he's not liking it.
This is why I always tell people when they first bring home a new bird that they need to locate their main-cage in the "main room" of the house, where the people that live there spend most of their time when their home, like the living room, family room, TV room, etc., because birds want to be "among their flock", after all, they are "flock" animals...So they feel the most secure, safe, and content when multiple people are around them! If you locate their main-cage in the room of your home where the people spend most of their time, birds are a lot more-likely to contently entertain themselves, rather than not being around multiple people...that's just the nature of their being as "flock animals"...So at your parent's house there were multiple people around him, and now he's either alone or usually just with you, and so he wants to direct attention without a "flock" surrounding him...
As far as medical school goes, yeah, that's going to be tough. I went through grad school for Animal Health Science, and I can tell you that it was challenging at best, and if I'm being honest with you, one of the reasons that I chose not to go to either Veterinary Medical School or Medical School was because I didn't think it would be fair to my pets...That was a choice that I made for myself because they are my family, quite literally...But grad-school was a nightmare at times, because I always made sure that my dog and my bird got tons of time with me, taking walks/runs, etc. So my life was pretty much a living-hell for 3 years, and honestly doing a BS in Health Science in one of the most demanding undergrad programs in the country was just as challenging as Grad School was (I had Gross Anatomy with Cadaver Lab my Junior year of undergrad, with classes from my Freshman year forward like Exercise Physiology, Organism Physiology, Biomechanical Physics, Advanced Pharmacology, Advance Human Anatomy, Advanced Human Physiology, Cardiovascular Diagnostics, Advance Neurology, etc.)...So making my pets happy and healthy was difficult, and I had to just make it work because I didn't have a choice, my mom wasn't caring for my dog for me, though she would have taken my Budgie back, but I'm actually glad I did it the way that I did, because he lived to be just shy of 19 years-old, so he was a special little dude...
All I can tell you is to say that this is a huge change for your bird from what he is used to, and their feelings that stem from their innate "flock dynamics" can create issues if they go from a situation where their are multiple people around all the time to suddenly being either alone or around only one person. He's going to be demanding of your time, and he may or may not adjust and start to feel more content entertaining himself with just you around, or he might not...I don't know what year you are in Medical School, but as already mentioned, when you start your internship it will be tougher, and even much, much, much tougher when you start your Residency...
