My guess is Posterior Tibialis - either the muscle or tendon or both.

You might try massaging the muscle.  A great massage is to cross your legs, putting the ankle of the leg to be massaged on top of the opposite knee.  You'll be looking down at the inside of the shin, with Posterior Tibialis pointing up.  Put your thumb, down by the ankle, right behind the shin bone, where the fleshy parts starts.  Wrap your fingers around the front of the shin.  Put the other thumb on top of the the first, and wrap your fingers around the shin.  Now make small circles with your toes, rotating only at the ankle.  With each rotation you should feel Posterior Tibialis relax and contract.  While continuing to make circles with the foot push your thumbs firmly into the flesh and slide your thumbs up the shin toward the knee.  The contracting and relaxing of the muscle will cause it to be massaged since you're pushing against it with your thumbs.

This might make the muscle a bit sore.  It should help lengthen it and relieve some of the tension.  You might try icing the area.  Sometimes temporary arch supports help take tension off the tendon.  If it were me (but it's not) I wouldn't do ibuprofen.  Some say it delays the healing process.

Jim

This sounds similiar to problems I had when I had a stress fracture in my tibia.  The pain was on the inside of my lower leg just above the ankle.  If I squatted or put any weight forward, there was pain.  If I pressed on the area with my fingers there was pain.  The strange thing was, however, that while the pain was terrible at the beginning of my run, after a mile or so, the pain went away (runner's high perhaps?).  But after a run, the pain was back with a vengence, like an aching pain.  When I went to the doctor, I was first told I had shin splints, and to just take some pain medication, ice down before and after a run, and run at my own pace.  I wound up taking motrin and continuing to run, thinking it would eventually work itself out.  Big, big, mistake.  This only make the fracture(s) worse, and after a while I went back to get an x-ray and sure enough it was fractured.  It took a very, very long time to heal, and even now several years later I still have problems when I try to push for distance, or up my mileage too quickly.  I suggest you rest and recover before continuing.  ~Cindy