Wow, I never knew that had a name! I used to get them a few times. Never knew what they were. But, I did some research and found out that toothpastes containing sodium lauryl solfate can cause mouth irritations like this and canker sores. I changed toothpaste to Biotene which has no SLS in it and ever since, I have not gotten any of what you have there or canker sores. Biotene also has a mouthwash and it's all sold at Walmart, Target..cost is more than a regular toothpaste...about $5.
Biotene is also recommended for people who have dry mouth. Dehydration.
Some info suggests these "lines" on your inside cheeks can be caused by cheek biting..maybe in your sleep. Not sure if I believe that. I doubt I bite my cheeks.