Flea Treatment for New Cat owner?

Hello, I’m a new cat owner, and just moved across the country. While I was moving, I had the cats stay with a relative for a few weeks until we could fly them out as we were worried about them surviving the drive across the country, and while they were staying there, they got infested with fleas.

I’ve got a dog at ho e that doesn’t have fleas, since she did fine on the drive, and we’ve got the cats quarantined in our bedroom. We bathed them with some flea removal soap, but last night I got completely bit up by fleas, so that didn’t fully clear it, and it means now they’re in the house as well.

I’ve read bravecto is recommended, but I’m not sure how to take care of the bed and area rug?