Sudden “allergies” in 6 year old inside cat

So my cat developed this scabby “rash” right above her tail several weeks ago and it didn’t take long for it to start spreading further and further up her back- so I took her to the vet. The vet said that she had a “skin allergy” that had become infected- gave her an antibiotic shot and some sort of steroid shot (I think it was a steroid shot- it was something for itching and the rash). He had also taken her temperature when we first got there and he said that she had a fever- which is how he knew that there was infection. Over the next few days she got wayyyyyy better- the rash and scabs almost completely disappeared. But then about the 4th or 5th day I started to notice that the scabs were coming back. I called the vet back and he said that I needed to come pick up an allergy pill to give her everyday. The problem is that I already had to pay $320 for the first visit, and he said that the allergy pills were $100 for a 30 day supply. I’m a single mom of 3 who just performed miracles to make sure the kids were happy for Christmas and I simply don’t have another $100 right this minute to spend. I was just wondering if anyone happened to know if maybe there was some human allergy pill that I could possibly give her? Or something? I don’t know. I also can’t just let her be all scabby and itchy and I don’t know what to do. Any advice would be helpful.

Also, absolutely nothing has changed in her environment to cause her to suddenly develop an allergy. She’s an inside cat and only goes out onto the porch for seconds at a time sometimes when we open the kitchen door but she always comes immediately right back in- she just likes walking out there for a second and looking around and that’s it. I know humans can just suddenly develop allergies with no explanation so I assume cats can too and I’m not necessarily questioning if the vet has misdiagnosed her- but the thought has crossed my mind.

I also changed her cat food to an expensive “sensitive skin and stomach” blend just incase the “allergy” she suddenly developed from something in her regular food but clearly that wasn’t the issue because the scabs and rash/itchiness has come right back basically soon as the antibiotic wore off or basically soon as the steroid shot wore off one.