I would say not to keep switching toothpastes, but instead find one you like. The skin peeling inside your mouth isn't anything to worry about. A lot of people get this. It is most likely your toothpaste your using, if it has tarter protection or a complete formula. Many people say they get it when the use Crest Pro Health. But, this type of peeling occurs from a mild chemical irritation and will go away after a few days of stopping the cause. It is like an unintended chemical peel.
Examples of causes are: water softeners, chlorine, mouthwashes, toothpastes with special detergents (such as tartar control or complete formulas), overuse of lozenges, mints, and chewable vitamins. You can also get this from taking powdered aspirin formulas and phenol containing agents.
Seeing a dentist is advised. Dental school will cost you much less.