Can you post a picture of that white line..?
Most likely, it's "Linea Alba".. Linea Alba is a whitish line that runs on the inner side of your cheek along the occlusion (biting plane)..
Typically, it's caused by chronic friction between your teeth and the lining of your cheek.. Usually this is a sign of irritation due to misaligned teeth or improperly done filling or cap..
Next Steps
There is nothing to worry about.. It's almost always harmless..
Health Tips
Get it checked by your dentist only if it starts giving any pain.. Though it's very unlikely..