I'm so very sorry that you lost your fid, no matter how this happens or where you are this is a horribly painful thing to go through; to not be there with them when they pass stirs-up all kinds of different emotions, guilt being a big one of those emotions...However, you personally know how strong and special the bond between a person and their bird is, and I hope you find some solace in knowing that no matter where you were during his last days or on the day he died, he was thinking of you and loving you, and he certainly was not thinking negative thoughts about you in any way. He just loved you, and this experience between a person and their fid is one that most human-beings don't at all understand, simply because most people aren't lucky enough to have ever experienced any relationship like it in their lives. That's a relationship and a love that you will always have and be able to treasure, and this makes you a very lucky person, and your bird a very lucky bird.
I can understand why people who have never had any pets at all in their lives, or that have never had any connection or experience with animals in their lives, can't understand the relationship, the bond, the connection between a person and their non-human family members. That's makes sense to me, though I wish that they would at the very least respect the relationship between a person and their non-human family members, even though they don't understand it. However, I will NEVER be able to even begin to understand how a person who has had an extremely close bond/relationship with a pet, whatever type of pet that might be, doesn't matter, how they very often tend to discount the relationship that another person has with a different type of animal/living creature than they have had...that makes absolutely no sense at all to me...And it's quite common too, it's not like it's a rare phenomena, which is what makes it so strange to me. If it was just a sporadic point-of-view that popped-up once in a while, in arrogant, narcissistic people only, then it would make sense and could easily be ignored, but that isn't the case at all. I've know many an otherwise kind, loving, friendly person that has held this point of view, and who has unfortunately been extremely vocal in expressing that point-of-view in a horribly cold, non-compassionate way, and most of the time it doesn't even occur to them how much this hurts the person they are aiming this attitude and opinion at...
And yes, it does tend to be dog and cat people (mostly dog people) who look-down upon the relationships/bonds that people have with any other types of non-human family members. Why I have no idea at all, as I have always had at least one dog in my life from the time I was a very young child and I have never put one of my pets above the others. It's not a "size" thing, as people who own horses and other huge animals don't tend to look-down upon any other pets...so why do specifically people who own dogs tend to discount the relationship between a person and any other type of "pet"? Who knows. And who cares. I myself feel sorry for anyone who doesn't understand nor appreciate the type of bond a person can have with a bird, a reptile, an amphibian, a rabbit, a hamster, a gerbil, a guinea pig, a horse, a goat, a pig, a cow, a suger-glider, a monkey, a ferret...hell, a fish. I'm not a cat person at all, I just have never formed that kind of close bond with a cat, nor am I the kind of person who wants a pet that is so independent. That being said, I certainly understand and appreciate that many, many people love their cats every bit as much as they love their human children, and every bit as much as I love my birds, my dogs, or my Bearded Dragons.
I'm so sorry that your sister was not supportive of you and didn't show you any compassion at all while you were going through the intense pain that you were right after finding out about the death of your little Conure. For anyone to tell you to basically "be quiet, stop crying, and go to sleep" literally minutes after you had been told that your bird had passed-away is just cold-hearted, and frankly just mean and nasty. For your sister to act this way towards you and to say those words to you is unthinkable, and then to also tell you that her relationship with her dog is somehow more important or meaningful than your bond with your bird could ever be, well, that's just an extra kick in the butt. There's no way to explain her behavior to you, as there is no explanation for it, and honestly it doesn't matter, It's just the way she is and the way she thinks, again not an uncommon take on this particular situation, and you're obviously the bigger person. And I know damn well and have no problem saying this, even though I don't know you, that when your sister's dog passes-away and she's devastated about it, you'll be there to comfort and support her through the whole grieving-process.
I hope that you're able to heal, and I hope you're able to take solace and find peace in all of the memories you have of your bird, and remembering how special the bond that you had with him really was. That's something that you will always have and that no one can ever take away from you.