Moving in with a cat owner but allergic to cats?? Help!!

My boyfriend and I are moving into his dad's old house, which have been home to two cats. Here's the problem, our son and I are both allergic to my boyfriends two cats. Within about an hour of being there, I can no longer be inside. I have to stay outside even sometimes after just a few minutes of being in there. I have asked if he will rehome the cats but he won't budge, which I understand. My boyfriend also is terrible with cleaning up after himself, so I cannot even expect him to clean up after his cats to atleast keep most allergens out of the house. I breastfeed and have heard that most allergy medication can affect supply, and we probably could not afford the constant medication anyhow, I also have growths in my nose that we cannot afford to have taken out, so even the slightest congestion sends me outside to clear up with fresh air. Unfortunately, due to  bill costs, we cannot afford to have Windows open letting out the cold air, especially in this heat. I am quickly running out of options as our move in date and end of our apartment lease comes closer. Help!!