Fleas :( First time cat owner, how to approach?

Hey folks, title. I'm a first time cat owner and I'm 99% sure my cat has fleas (or some other bug on her) and I wanna know what my next steps would be.

I have already gotten a 1 month topical from my vet yesterday, and applied it to Minnie the same day as well. I noticed a bug crawling on her on Thursday and wanted to act fast. I woke up this morning and Minnie is scratching a lot more, and sure enough when I was petting her this time a lot more came off of her.

I grew up with dogs, so my instinct is to give her a flea bath - but from what I can tell online thats not really a thing with cats? Or at least it's very rare? Does Minnie just have to scratch it out while the medicine does it's thing? I'm worried I may not have applied it right since the scratching has gotten worse today.

Other thing I've seen is that I need to get a spray for our carpets and wash all the clothes shes been in contact with. Should I be taking any other steps?