While it's true that some people with compromised immune systems may be more susceptible to some infections from some animals, giving up beloved companion animals isn't always necessary. Talk to your veterinarian and physician about what you can do to keep yourself, others, and your pets healthy. You can keep your pet. Sometimes love is the best medicine of all. I've had pets all my life and never had any problems.
Pets can carry zoonotic infections, that is, infections that are shared by people and pets.
Because your resistance is low, you are more susceptible to these diseases now. But the good news is that you can minimize your risk by working with your veterinarian to test, medicate, and care appropriately for your pet. There is no evidence to suggest that dogs, cats, or birds can carry or transmit HIV to people. Thus, for you, the advantages of pet ownership may far outweigh the risks. You will want to gather as much information as you can so that you can make the decision that is best for you and your pet.