I have a cut on the inside cheeks of my mouth from nighttime teeth grinding. What should I do?

Nature will heal it. There's nothing to do. Your body will heal it quickly. Avoid spicy, hot and acidic foods meanwhile. If it's a chronic problem have your dentist take a look at your teeth for any sharp areas that might need rounding off and ask if he\she thinks wearing a night guard would be a good idea for you.
See your dentist. You probably need a night guard and also some smoothing of some teeth. Sometimes the tooth cusps (points) are too sharp.