When i run my leg hurts in the back, a little under my calf. is this my running shoes or something serious?

Could be serious: You should see your doctor. From the area described it could be tendinitis, strain of the lower gastroc/soleus, or even a stress fracture.

May have injury: Most, non traumatic, running injuries/discomfort are secondary a combination of: overuse, foot function/structure, shoes and training surfaces. See your doctor for an evaluation and discussion. I would recommend you stop for fitness activities, stay in good shoes and supports, antiinflammatories as tolerated until your doctor visit. Dr. L.

No way to tell: If the pain persists you should be seen by a doctor to determine the cause.