What do you do if the wall of the vaginal wall is swollen and has a small cut I know how it happened but will it heal on its own I don't want anyone to know please?

As long as the cut was not caused by anything that is likely to cause an infection then don't worry to much the vaginal area has a really good blood supply which helps healing. If you have any fever or nasty smelling discharge then you should go and see you doctor . Don't be embarrassed .