The corners of my mouth have been cracking and healing over and over again for 3 months. As well as my lips burning and becoming severely chapped.?

Micro infection, dry. Sometimes dryness causes cracking at corners of mouth, and they become infected with fungal organisms. An anti fungal, topical, can often clear this up. Increase water intake and moisturize lips with chapstick to keep them moist. See doc if problem persists. Doc will have to prescribe for anti fungal.