Possibly shinsplints. Rest and Ice are pretty much the only way to get rid of them, unless you have access to a muscle stim unit, in which case you can use that to help speed healing.
Definitely get some good, high quality running shoes. Moist heat preferably before you run to warm it up, stretching before and after, and ice preferably with elevation afterward.
Just give it time, and you'll be ok. At least you're not like me; I had to run an entire cross country and football season with shinsplints, no time to rest.