Can you get mouth ulcer from burning the inside of your mouth on hot foods?

Yes: The mucosa in the mouth is extremely sensitive and extreme temperatures as well as friction can cause oral ulcers. Avoid hot and spicy food for about a week and it should go away.

Yes: Pizza burns are very common on the palatal area. It usually is self limiting and heals within a couple of days with or without treatment. A topical anesthetic like Benzocaine can give you some relief and is available over the counter.