How do you know when it’s time to give up a pet? (human health problems!)?

I have two parakeets–one of them I’ve had for around four years, the other one I got about a year ago. Since we got the new one, my mother has gotten double pneumonia and had to go the hospital, and I’ve had bronchitis five times already. My doctor and the hospital said it’s most likely the birds. I try to keep the cage as clean as possible, and I’ve got an air purifier too. But I’m just soo busy with school now and life. I have little time to take them out, and I also have to make time for my rabbit (who is not the reason behind the respiratory problems. its not allergies, it’s more related to psittacosis and bird flu illnesses)
I’m in my junior year in high school and I know I’ll be going away soon, another factor to consider. But I’m also centering my career around animals (I want to be an animal behaviorist) and I feel giving up pets I chose to take in would make me the biggest hypocrite in the world. How can i start a career with animals when I can’t even take care of them at home?

The parakeet owner’s handbook;: An easily followed guide to long life for your parakeet; showing how to most quickly train yours to talk; how to breed … diseases promptly; a human interest handbook