I have a rash that appears on the inside of my elbow that itches and then goes away for few weeks. What is it?

Could be eczema. This rash sounds like it may be an eczema type rash- which typically appears on the skin folds (especially elbows and knees). Try hydrocortizone 1% cream a couple of times a day when you are having the rash/itching. If the skin is dry, try a good moisturizer such as eucerin, cetaphil, cerave, or even vasoline.
Eczema. The appearance of eczema can vary from person to person. In adults, eczema occurs most frequently on the hands and elbows, and in "bending" areas such as the inside of the elbows and back of the knees. In young children, eczema is often seen on the elbows, knees, face, neck, and scalp. Treatment is with topical prescription cortisone and emollients like cerave cream.