My baby Desert Tortoise has peeling around his mouth.

by Samantha
(Goodyear, AZ. USA)

Hi everyone! I'm a new Desert Tortoise owner. I have a baby, he's about five months old. (his name is squirt)

Today my boyfriend noticed he has peeling around his mouth. We read online it's a nutritional problem. :(
I would like to know what the best a fastest way I can get my little guy back to good health.
Here's how I take care of squirt, so you guys can tell me what I'm doing wrong.
Right now he lives in a little ten gal. tank. I have natural soil as bedding so he can eat the dirt for his tummy. He always has fresh water. I feed him the mixed salad box you can buy with the red lettuce, spinach, and all that good stuff. I also feed him petunias. I try giving him carrot shavings but he won't eat them. He does on the other hand, eat like a little piggie. He'll eat two or three handfuls of the mixed salad a day. And he's small, like smaller then a wallet. He has a UVB bulb. And before winter was here I took him out in the garden everyday. (I live in Arizona, so winter is pretty much almost over)
I was already thinking I needed to widen his diet. Now that I know he isn't doing well though I would love some help.
Also I have some vitamins I use for my lizards. It's calcium with D3. Should I try and give him some food dusted with it? Or is the D3 not good?
Thanks guys!