Parenting isn’t for the weak

My girlfriend and I have a baby together, got a cat few months ago. My other kid recently got diagnosed with asthma and the doctor may think they’re allergic to the cat and it’s causing a flare up. Girlfriend thinks otherwise, and thinks it’s no big deal and my other child is fine. I am taking precautions and not taking my son to my home while we have a pet cat. It’s an easy win to me , I know we should get rid of the cat. Girlfriend tells me I should be the one to go. Honestly she may not be wrong especially after giving that answer (child who may be allergic is not my girlfriends child)