Could you give me some suggestions for getting rid of shin splints?

Multiple things: Orthotics will help if the underlying reason is flat feet. Proper running mechanics play a large role as well. Sometimes silicone heel cups and a stretching regimen can do he trick too. The orthotics don't necessarily need to be custom. Otc types will usually work.

Shin splints: Aspirin or NSAID's, ice after activity. Orthotic devices if feet are abnormally flat . There are compresssion sleeves designed just for the leg; they go from below the knee to above the ankle. If you don't get better, consider a stress fracture of the tibia; x-rays, bone scan or MRI would help diagnose.