Yep, probably shin splints but do not eliminate the possibility of compartment syndrome or stress fracture if it begins to hurt all the time.
Orthotics are a good idea like someone else said, I got mine from orthoticsdirect.com and they work well. Also, get some good running shoes with motion control and I would invest in some good, padded socks such as Thor-Lo. The socks are expensive, but quite worth the investment.
While typical physical therapy protocol for shin splints calls for exercises such as dorsiflexion with resistance,picking up marbles out of a bucket, and towel pull-ins with your toes to strengthen the anterior tibialis, from my experience these aren't THAT effective. They might be worth a shot though.
If you want to do this, though, find some exercise tubing or some Theraband ( or some form of "elastic" resistance), sit down or on a chair, put the band or tubing around your foot and flex your foot towards the body, thus feeling a contraction in the area affected. If you can't find any tubing, you could do this without any but I don't know how effective it would be.
For the marbles one, just get some marbles, put them in a bucket and sit in a chair and pick them out of it with your big toe and the one next to it, and set them on the ground until you have removed all the marbles (around 50 is good). I have actually heard people say this is pretty good.
The towel pull-ins involve just sitting on the floor, putting a towel down, and using your toes to roll it in, then repeat.
Sorry I don't have any pics of these exercises, but please ask more Q's if you need further explanation.
Also, get some frozen vegetables (in the bags) and ice your shins a few times a day, esp. after running when you get to where you can again. For now, stick to non weight bearing exercise like the elliptical until the pain subsides and you get some orthotics, good shoes and socks, and maybe do the above exercises for your shins.
Ibuprofen is also a good idea to reduce the inflammation after you run.
Hope this helps, and good luck getting back. Shin splints suck, but I got the orthotics and good shoes and socks and all of this worked wonders for me. Not pain free, but a lot better.