Can an injury (eccept a broken bone) heal by itself with no treatment?
Yes. Broken bones heal themselves too; surgery is sometimes needed to actually position the bones so they recover the right way. Happens a lot with nose fractures or broken noses, people need to get surgery so that the bone recovers in such a way that it’s not an obstacle for your breathing. As for muscles and sprains, these heal by themselves and all but remember to cooperate with their recovery. Sit still, lay down; whatever will keep you from moving your injured muscle. Muscle is formed by fibers; they are many strings that keep the muscle together.. a sprain is caused by a rupture of one or more of those strings. It takes a while to heal completely but it does heal.
