Will salt help wounds in my mouth heal?

No. What are you trying to heal in your mouth? Have your doctor or dentist look at them or if any thing has been operated on check with surgeon.
FAst Healing. The good news is that area has fantastic blood supply and so healing will occur rapidly. Inflammation (red, hot, tender swelling) is the body increasing the blood flow to the injury to bring healing factors to the area and also the veins expand to carry bad stuff away. Dressings and ointments are of no value there. Avoid further trauma to the area and let nature take it's course.