I also have the same condition with a thin white line on both side of my inner cheek. My Doctor said that white line was caused by friction rubbing my teeth with inner cheek side, whether intentionally or unintentionally. Intentionally I wouldn't do that, otherwise I would have been aware of it. I guess it must be my teeth grinding episode during my sleep.
Initially I thought it could be a sign of benign tumour or pre cancerous signs, so I asked my family Physician to do a mouth swab test for me. My results turned out to be negative which means I don't have any of those benign tumour or pre cancerous cells on my cheek. Surprisingly there is no cure for such condition. We can just hope it goes away on its own.
It is easier if we can stop grinding our teeth against inner cheek intentionally but sometimes unintentionally during our sleep, we cause the white line to appear, due to friction between teeth and inner cheek.
Another physician told me that it could be due to fungus or bad bacterias inside my intestine that is causing the white line to appear in my inner cheeks. The Doctor prescribed me anti fungal tablet which I had to take only one time. This tablet didn't do much. I was asked to gargle with salt water regularly but this didn't do much good either. I was also asked to eat more of Yogurt because it gives me good bacteria. Now, this yogurt eating helped me a bit but it didn't completely remove the thin white line in my inner cheeks.