Is it possible to glaze a mug that has been glazed already?

I bought a mug from michael's and painted it with porcelain paint. It is non toxic but just to be safe i want to put a clear coat over it and fire it in the oven so that I will be able to drink out of it. I asked a ceramics teacher if i can glaze the mug and she told me that if i glaze a mug that has already been glaze then it will run off. Is this true? if it is, can anyone offer me a different solution'?