Chances are it'll be shorter your whole life. Not sure where it's shorter, but I have a 1/4" difference between my leg lengths (left is shorter).
When I was growing up, my folks talked to a doctor, and he suggested that they get me a lift for my shoes. It's a removable wedge, leather with a soft upper surface, that fit into the heel of my left shoe (removable so you can change it from shoe to shoe). This was mostly so that I'd grow up with a straight spine, since the shorter leg tended to make my pelvic bone tilt, which affected my spinal alignment. Since I've grown up, I no longer bother with a lift, but notice the difference in length if I'm standing up.
So far as custom shoes, it's pretty much a given that you should wear the best shoes for running, especially since it is so darn hard on your knees. A removable lift would likely shift around inside your shoe, causing discomfort, and getting one built into the heel of a pair of running shoes would be expensive.
My suggestion would be to go see your doctor, make certain it's not something else (bad knee), talk to a personal trainer type person about your running style (make certain you're not doing something that's causing the pain, without even knowing you're doing it), and possibly consider some other form of aerobic exercise that's easier on your knees. 🙂
