Shin splints are common during plebe summer. At 0530, you'll go to physical therapy instead of PEP if you say you have shin splints. They'll probably give you a chit that exempts you from PT, chopping, drill, and pretty much any other physical activity for X amount of time. Furthermore they'll probably tell you to come back to physical therapy instead of PEP for a while. That's how they're "handled" -- physical therapy and chit until you're better.
Now, that brings up an interesting point about chits... YOU DON'T WANT TO BE ON CHIT. Unless you absolutely have to. I've seen someone run through shin splints. He struggled but survived. I saw a girl who was on chit for half of plebe summer because of "shin splints" and that made her look really, really bad to both the detailers and her classmates. Best advice I can give you is not to overexert yourself and be smart during the runs. Don't go too slow, don't kill yourself. You don't want to be on chit unless you absolutely need it. You'll have to use your own judgement.