Trust me, STOP RUNNING!!!
I pretty much ended my amateur boxing career because I wouldn't listen to people when they told me to stop running when I suffered from shin splints.... I said "Eh, I can take a little pain. Don't wanna fall behind" so I kept running through the pain....
.... and after a year of running through the shin splints, ignoring the pain, one day I collapsed and couldn't even walk. I had to lay there all day until I could finally get to a phone. Now the damage that I've done by ignoring the problem is permanent.... and if I start running again, even on grass or a soft surface, the shin splints return after only a day or two. I had surgery, but still can't run for more a couple of times without a few weeks in between.
I learnt at uni that by ignoring shin splints and continuing to run, you do damage that is irreversable. I wish I'd known before.
Please, don't run with shin splints. Bad idea.... you'll ruin yourself. Do some stretches for tibialis anterior, and talk to a specialist about what else you can do to prevent them.... but don't run until they say it's okay.