Young cat self-mutilates (bites herself)

Someone please help.  Has anyone had this experience or anything like it?

My cat is 19 months old and 7 pounds. I gave her and advantage treatment and then a month later was ready to give her another when I noticed scabs and cuts on her back around the shoulders.  So I took her to the vet. The vet found flea dirt and concluded that she was allergic to the flea bites.  She was given shots to calm the itching and antibiotic shot for the cuts.  You would think all of this would have worked but when we took the E-collar (cone) off she was back at it biting.  (This was after treating the entire house twice and applying Advantage every 3 weeks.) Next they tried to get me to give her Prozac but I just couldn't shove it down her throat.  I'm stabbing in the dark now thinking it's her food.  She lives with her E-collar and is quite happy with it on.  She's totally weird when it's off.  The vet now thinks it's a behavioral problem.  What do I do?

Are you sure it is not an allergy? Did your vet do tests? 

I have a friend who had a bird that was pulling all the feathers off of her neck.  They did the collar thing for awhile too and eventually went to the bird version of prozac, whatever that might be, that seemed to do the trick.  It was some sort of anxiety issue.  They were eventually able to wean the bird off of the drugs.  They just have to kept a really strict schedule with her or else she will start to get nervous again.  I would try to find a way to get your cat to take the prozac but I agree that allergies need to be ruled out first.

Vet didn't suggest the allergy tests but they are cost prohibitive

That is true. Well, if you go with the vet, instead of prozac why not try more natural calming remedies? That is if the signs show your cat is over anxious without the e-collar. If you suspect allergy, you also need to find and get rid of the allergen. If it is food, did your cat's reaction start when you changed or added something in her diet? Are you using a different soap, cosmetic? Anything new at home?

A FB friend posted that she could not find what was making her cat itch all the time for years. After trying everything, by chance she found her kitty was allergic to the dog. Her cat and her dog often slept together and the allergies always happened during those times. 

Did you get rid of all the fleas?