I got sun burned. When will my skin be normal again?

Several weeks. Most likely it will take several weeks for the sunburn to totally resolve. You may experience some peeling off the skin depending on the degree of the sunburn.
What Degree of burn? All sun burns can cause permanent damage to your skin. First degree burns are usually self limiting. You need to stay away from the sun until the skin completely heals. Second and third degree burns may cause permanent damage such as discoloration or post inflammatory hyper pigmentation or scarring. Stay away from the sun from 10:00 am to 2:00 pm. Always use a sun screen with a high SPF rating.