It sounds like from your description that she is over grooming herself. My sister has a cat that does that and as a result of the excessive grooming she has thin spots of hair on her back. Many times it is caused by stress. My sister just moved into a new place and moved the kitty inside exclusively. The kitty's hair loss increased significantly. She was also being picked on my their other cat that was also now confined to being inside at the new place. You mentioned that she is always licking herself and that she is happiest when she isn't around the other cats. Could you perhaps keep her separate from them, like in her own room or something so that she wouldn't have as much stress? There are medications, both by mouth and some by air that help calm kitties also. You mentioned that you didn't think it was allergies because your other cats didn't have the problem. Not all cats are allergic to the same thing, just as two humans in the same household don't often have the same allergies. I'm just taking a guess about the over grooming being the problem, I'm sure a vet visit would be more helpful in diagnosing her condition. I do understand the limit in funds at the moment too though. Perhaps you could try separating her and see if things improve.

And, welcome to Pet Talk!