Is it normal for only one side of my uterus to bleed?

How can you tell? A woman can't see her uterus. She can't "touch" it (except during pregnancy). No matter which part of the uterus bleeds, the blood drains down through a single hole in the cervix. That means there is no way to tell where in the uterus the blood is coming from. If there is very little blood on a tampon, the blood might stain only one side of the tampon.... But that would not be a sign of illness.