Yes, it is possible to get chickenpox again. However, this is an unlikely event since the virus only activates once but if it becomes active again it cause a viral infection referred to as shingle. You should go see your doctor for a check up to determine the cause of the itchiness.
You can only get it once. After that you are immune. Your body has the immunity to the virus after the first time.It can no longer affect you. You can however get a different strain of a similar virus with the same symptoms. But chicken pox, One and done.