just found a flea on our cat, do we go full nuclear?

Our cat Athena is a fluffy girl and we just found a flea on her, we removed it and crushed it but now my girlfriend is freaking out and her skin is squirming thinking the whole house could be infested. I'm of the opinion that we've caught it early and we should just check her usual sleeping spots as well as get a flea comb but my girl is damn near ready to buy a steam cleaner for the rug.

Idk, what do you guys think? How should we handle this?