I've had pains similar to the ones you're describing, and it does indeed hurt when I press on the inside of my lower leg. I think it is the problem described at the top of this page, what he calls "Medial Shin Splints."
http://www.drpribut.com/sports/spshin.html
And then again here.
http://www.unc.edu/student/orgs/sata/june2000.html
I think that the first page's advice to completely take time off should be taken with a grain of salt. I got custom made orthotics which seem to be pretty helpful when I wear them (I can never quite get them sit just right in my shoes), and I stretch and ice the spot a lot. I seem to get the pain with varing degrees of severity in both legs. I've found the best way to stretch it out is by squatting down on the balls of my feet.
I don't know too much about this besides what I've read on a couple websites and dealt with myself, so I'll be eagerly checking back to see if anyone has anything to add.