I just started running and when I run, only, my shins really hurt. The sides get really sore, almoat like shin splints......Any adivce?

Tight muscles. These muscle groups in the leg are attached to the tibia and fibula and actually pull on the bone when they are tight. Stretching these muscles passively (non-weightbearing) will allow the muscles and tendons to elongate without injuring them. Theses stretches work well with the use of elastic bands.
Slow down both in -- Intensity and distance you run, by a notch or two. Then start slowly and gradually increase the distance, ir the time frame you run for, or the intensity with which you run. So slow down. If it continues, see your pcp.
Need to stretch. You need to stretch your calf muscle--- e.g., runner's stretching exercises, before and after running or exercising. If your symptoms persist, please see a foot and ankle specialist (dpm , do, or md).