cat licking hair off her body

[thankfulheart]

My 12 year old female cat started licking her side about 6 weeks ago...over that time she has licked all the hair off the side of her body and leg and her belly. I've taken her to the vet twice...at first they said she had fleas...she didn't. Non of the animals do. Now they are saying she has probably developed a food allergy and we have to avoid a whole list of things or get the rx food they sell... Has anyone every had this issue? I'll be heading to the store to read labels soon...I don't even feel like this is the problem, but I guess I need to try to find food and see. They say it can take a couple months to know a difference!
We moved in October, so we thought at first it was stress and the vet had us use a feliway plug in to see if it helped and it didn't. I thought it was odd that if it was stress it happened 5 months or so after we moved. She was fine until one day I noticed she had a little patch gone on her side...and then it just went from there. She's not damaging the skin, just licking her hair off.
I do know that not long before I noticed this, we had given her a little dry food at night to try to keep her from waking us up to eat...so maybe it was a food allergy triggered by that? They dry food didn't work, so we only did that as long as the bag lasted and quit. They wake us up I think just because they can. They are extremely spoiled...bottle babies from day 1 and I'm not sure they know they are cats. She's really looking bad and now she's started on her other side, so I need to figure out what to do for her. Other than the excessive grooming she's perfectly normal. I don't even see her grooming much. She must do it mostly when we're in bed. I'll try to post some pictures in a little bit.