Hello. It looks like a oral lesion than a cut.it may be associated with burning. Kindly take prescription medication after  examination. And history of lesion.

The white lesion in your mouth is typical Lichenplanus / lichenoid reaction. It is a chronic condition. Regular follow up is necessary to monitor. If you are keeping any chemical agent in your mouth to relieve pain please stop it.

A long standing white lesion should be taken for biopsy. Is it painless?

Hello. I would advice kenacort oral gel. Apply this gel every 2 hourly, and 5 minutes before you eat your meals. Don't rinse after applying the gel. Do warm saline rinses. Add salt to warm water and rinse with it. Hold the water on the side of the cut for 10-15 minutes before spitting it out. It will burn a lot initially but will definitely cure the cut faster.