The same sort of thing happend to me about 3 months ago when I started running to get in shape for baseball, except it was my knees that were sore during it, but not after. I found that if I just ran on a regular basis, it went away after the first 3 or 4 runs, perhaps my knee joints were not conditioned for running, as perhaps your shins aren't. Anyways, I would start of running as slow as you have to to get a mile run in, and then work on distance first, not speed. This will help you get endurance, and then after a while you can mix in some speed changes. For example, I run about 4 miles usually at a pretty slow pace, but one of the miles (after I'm warm) I run at about a 6:30-7 min pace, timing it to push myself the next time I run. Hope this helps!
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