When Running Is Not OK. Soreness can be caused by strained or pulled muscles, and running can make these problems worse. If only one leg hurts or you have sharp pain anywhere, do not run. There are a number of other symptoms that can signal your need for rest.unning can cause further damage to your legs and you won’t get the health benefits that running brings if you have to shorten your routine due to pain. If you do decide to go running while you’re sore, taking some precautions will help get you back into shape faster.