To answer your question more directly, no there is nothing safe or effective to use over the counter to clear up mange in cats.
Unfortunately you do need vet help for this problem, but the good news is you may just be able to get SELAMECTIN (Revolution®) to use to do this instead of trying to bath the cat or bringing her in for painful injections. It appears to clear up both sarcoptic mange mites which cats can get and the cat type notoedic mange mites too.
Hope this helps you!
It does not survive off of the cat for very long so it doesn't live or breed in carpets.
But ringworm fungal infection can lurk in carpets and home to infect another pet.
You can read about that here
I'd suggest starting with asking another local vet for the cost of an office visit and a skin scrape. If its mange you can ask about using Revolution and they make that for dogs too which would clear your dog of mites if the dog has picked them up.
You can read about how ringworm is treated on the above site.What you want to know when you call a vet is how much for an office visit, expected/estimated costs to diagnose a possible skin parasite to decide if you can manage the costs.
As cash flow is an issue Cher (jessesmom) did give you a link with lots of potential financial resources but you might also check with your local humane society about low cost vet care in the area or consider seeing if you qualify for Care Credit so you could do time payments for care
http://www.carecredit.com/A credit card company for health care, including veterinary care."With a comprehensive range of plan options, fortreatment or procedure fees from $1 to over $25,000, we offer a planand a low monthly payment to fit comfortably into almost everybudget." They have a zero interest program if you pay within a certain time frame and they list the vets who work with their product.
The thing to know is vets all have different fees as overhead is different and so their pricing may reflect that. You can shop around a little by phone and ask about basic costs like office visits and shots etc. to see who seems most reasonable to work with.
Let the vet know your budget is tight and they will often work with you.
If you found an answer helpful you can accept it and thanks!