My leg and arm on my right side are swollen what causes this.?

Can't say. Swelling of the arm and leg on one side is usually due to 2 separate causes. Do you have other symptoms?
Doctor can evaluate. In order to swell up just on one side, there has to be more blood or more fluid in that side of the body. The primary care doctor might check to see if there is a blood clot or blood flow problem, if there is a problem in the nerves or nerve signals to that side of the body, if there is fluid in the tissues that is settling into one side of the body due to gravity or lymphatic blockage, etc...