I need advice

So my mom has been suggesting we sell/re-home our birds. One is blue-fronted amazon and the other is a prince of wales parakeet. Recently the amazon has been biting me quite a bit, which is a problem because a) it hurts, b) it draws blood, and c) I don't need any more scars on my arms. My mom also finds it hard to give them attention. Since I'm on break from school, I usually spend a lot of time with them. They have recently been fighting each other. I am scared one day the bigger one by accident will kill the other. I have left the room for a few seconds to come to hear screeching and snapping. I love both of them and I have had them since before I was in kindergarden, but I can't be constantly separating them and being bitten.

Another thing that came up was potentially adopting a cat. We had one at one point, but that cat bit me and kept vomiting and peeing everywhere. At a local rescue there is this cat with one gold and one blue eye. She is pure white. It also describes her as a lap cat. I really need a pet that will sit with me and that I can hold. It would help with my anxiety and depression. I don't have many close friends and a lot of the time I can't go to them with issues for one reason or another. I spend hours at home alone and I can't particularly spend it with my birds because the parakeet hates me and the other one is constantly biting me.

The options are: keep the birds, keep the birds and get a cat, or get rid of the birds and get a cat. I need a pet that won't bite me. I also like lap pets that want to be held. I love those birds dearly, but it is coming to the point where I'm questioning if I'll have to get stitches because I was bitten by the larger one. I have no idea what to do. If you have any ideas, let me know.