What kind of cheek piece is it? Loose rings can catch the lips when they slide. Bit guards can solve this if it is the problem. The mouth piece could also be too short or too long, or too large/small in diameter and is rubbing. Also check if the bit is dirty or starting to rust. Wash it anyways, because if you cleaned it with something that was corrosive/toxic (like polish), or the soap, etcetera didn't rinse off completely when it was last washed.
Check bridle fit, too. Leather can shrink in cold weather, or if you've recently bought a new bridle it could be needing adjustment.
If it isn't the bit, it could be your hands. Critique yourself honestly or ask your trainer to assess your hands and give her opinion.