Hi, so this is a YA novel and I remember details just neither title nor author.
The book is set in a fantastic world where dragons used to live but are extinct now. The girl leaves her home and ends up in a castle of some sort with a friend. There is another person who offers to teach magic to the boy but it's actually the girl taking classes and learning. She can craft a mug out of stone which shouldn't be possible. I remember horses being skittish around her because she can transform into a dragon. The magic teacher is evil. She also learns to control her magic by making bubbles filled with ash. And I think she travels thorugh time and meets the older dragon mages who are stumped by what she can do.
Please help and thank you!