Ivermectin will work. People may yell at me for this advice but you can purchase equine (horse) Ivermectin paste on Amazon for under six dollars. Get a small blob of the paste and try to get it on the inner portion of the cat's ear. It will absorb this way. Or if you can't do that just get a blob of it anywhere on the cat. The cat will lick it off. I've had tremendous luck with it in rescue for feral cats that can't be handled. Ivermectin is, for the most part, safe. Just don't apply it every day. Evaluate the cat's progress weekly and if necessary apply it every seven days. If you can't afford the Ivermectin PM me and I'll get it for you.
To be clear, there are much better ways of handling mange in a cat. However, on a budget for a feral cat that can't be handled, equine Ivermectin is a very good option when administered correctly.
This is NOT how I would treat a housecat or a cat that could be handled.
If you can actually touch her take her to a vet and have them test her. There are different types of mange that require different treatments and other skin conditions that look like mange, but are actually something else.What’s the best course of action here? She let me brush her, so maybe I can still use a topical solution on her? What topical treatment is appropriate here?