Cat keeps licking stomach to it bleeds!

Hello all..hope everyone is doing well. I have an issue that I need help with. I have a sweetheart of cat and love her dearly. She has a sister who has had some agression problems, that we are currently dealing with and originally the licking we thought was a reaction to her sisters agression. Somewhat of a OCD issue...

Here's Lilly's info:

Lilly is a 3 year old shorthair who's in good health. She has a great appetite and we feed her Iams food 1/2 can a day (1/4 in the morning 1/4 at night). She used to be feed more and have dry food to eat everyday but she was overeating..so our vet told us to cut out the carbs and change her from Friskies to Iams. Lilly is an sweetheart and a lover. SHe wants to be around us all the time and whenever she can she's on my lap purring away.
Lilly has been licking her tummy for a few months now and has removed all the hair so it's pink. She has even created a sore which she's had for a while. We took her to the vet and the vet felt it was mental..so he gave her a cone which she has had on for 3 months (poor kitty) and Animax cream. It started to get a bit better, but any chance she gets she licks it and the scab would be torn off and were back to stage one again. We took her back into the vet and he gave her Elivil...as well as out agressive cat and she's a little better but still licking. I'm really worried about her and I wonder if she's allergic to something. She's miserable (cone on her head for 3 months...sorethat won't go away.) With all that's going on she still gives a lot of love and keeps her spirits up. Today I'm taking her again to the doctor to get tested for Allergies....

Can someone help? What's going on with my Baby? What's wrong with her? Why is she licking over and over....does anyone else have a kitty that does this? PLEASE HELP!!!!!!!!!!!!


DAVE