Usually a rash on the inside of the arm is a direct result of being exposed to something that may be an allergen to you. Did you go outside recently or do something that was different. Also keep track of what you ate. If you ate something different, that could be the cause.
All rashes should be diagnosed by a doctor too many of them look alike but are caused by totally different things.You should call your doctor tell them wht it looks like and that see is they want you to come in or they can diagnose over the phone.
You may have rub up against something that irritated your skin and caused a rash or you may have used something in your laundry that has caused it. If it is concerning then you need to go into the doctor and see what they tell you could be wrong with it.
It could be ringworm, fungus or simply a normal rash. If it doesn't itch you still should check in with your primary doctor or dermatologist for a prescription. Also you could go to the pharmacy for some rash cream