I've had long periods of running training, and recently picked up lifting.
I never got such pain from squats or deadlifts.
If I start running a fair amount again, I get shin splints.
Depending on your level, you don't need much volume to get it... Just take a few days off and run for shorter distances at first.
Don't forget to stretch. Irishman mentionned a few things but I have never tried them myself, apart from taking time off and having a shorter stride. Good luck!