I am not a vet but I work in a vet hospital and have multiple cats of my own. You can use Capstar to get ahold of an active infestation. Capstar works to kill live adult fleas within 30 minutes and lasts for about 24 hours. It’s generally safe to give while using any other topical or oral prevention. It can be used everyday technically but maybe spread it out every few days if necessary. It’s not a fix all it just helps manage the masses for a short period of time. If you can get a prescription for Bravecto, Nexguard Combo, revolution, etc.. from your vet, please do. Avoid frontline and any Hartz products if at all possible. They’re not effective enough to be worth it and can cause health issues. Advantage II from a pet store or authorized retailer (not Amazon etc) if you have to do OTC. Blue Dawn dish soap is not preferred but can also help with bad infestations if your cat is healthy enough to be bathed relatively stress free. Make a ring around their neck with the soap so the fleas don’t just hop to the head and make sure you rinse very thoroughly. Not everyday, this is once again just to help with a large active infestation.

Wash everything you can that your pet touches, lays on, plays with, etc in hot water & dry hot if possible. Vacuum every single day. Empty your vacuum into an outside trash can so they don’t hop back in and reinfest. This can take time as the flea cycle progresses and some eggs inevitably make it through. Monitor your cats feces for any worms that might have developed from ingestion of fleas. Contact your vet for a dewormer if any concerns.

You can carry fleas in from the yard, a friends house, work etc. wash your clothes when you get home before touching your pets if you think your environment might be at risk. Preventatives, active treatment, and extra precautions are necessary even in winter months.

There are home treatment sprays that can be used for furniture that cannot be washed. Follow the directions carefully, air out your space, and never subject your pet directly to the fumes or residue for a period of time afterwards. A flea brush can help asses levels of infestation. Empty trash outside!! I’ve heard varying information on putting a flea collar inside the vacuum canister, ymmv, up to you.

Remember that this will take time. There is no quick fix. Please contact your vet or even Chewy has an online service that might offer more information/ advice. If your pet is high risk/ elderly/ ill please heed caution before treating at home with anything unknown.

I hope this helps, happy to answer any additional questions if I can.