I’ve been dealing with shin splints on only my right leg (they are on the inside but I think they might be anterior shin splints, I’m not totally sure).
I’m doing this exercise I read about that is helping: Gizmodo’s shin splint exercise
At the same time I know something is off with my biomechanics. I’m working on my running form in general, and also improving my toe/foot strength and improving my hip internal rotation range of motion (I have really poor control of my toes it turns out, and not enough internal hip rotation). That stuff I learned about from the FootFunction Reddit group which I’ve found to be a great source of information.
My shin splints have gotten much better since I started that exercise above so I recommend giving it a go, I don’t think it will hurt!