I have a precancerous lesion in my mouth, would I get cancer?

See your doctor. Any whitish lesion in the mouth that doesn't go away with brushing should be checked out (leukoplakia). If it is suspicious, get it out. The oral pathologist will determine whether further therapy is warranted.
I'm surprised. That you are 22 and have a pre-cancerous lesion, but that means that if conditions (smoking, alcohol, where you use your mouth) and what you do about the extant lesion will determine if it progresses, invades or travels to other body parts.