Cat prozac

Has anyone had to put their cat on Prozac since bringing their baby home?

My cat pooped on our big lovesac a couple times after we sat their with the baby so we stopped sitting there and then she peed all in the baby’s activity mat so we threw it away .. and then this week she started peeing outside the litter box and it smells like she’s spraying. She did it all over my side of the bed today after I chases her away from the new activity mat. So I had to throw away my sheets and comforter and pillow - the stink was so bad there’s just no way it’ll come out. We had her at the vet yesterday to check her physically and $236 later they said she was in perfect health- blood and urine came back fine. They suggested Prozac so I’m gonna call them tomorrow and get a prescription. Please someone tell me it helps. Idk what else to do. I can’t have her peeing all over everything and I obviously can’t change the fact that there’s a baby in the house. We keep basically the entire downstairs baby free ever since she started pooping in the lovesac so she has a safe space. It’s not like the baby is brand new either- she’s almost 12 weeks old so idk why this crap is starting now. She isn’t aggressive or anything toward the baby- she jumps up while we feed her and rubs her face on her. I just don’t know what to do.