Remember our body is one giant kinetic chain with fascia (the netting that keeps us all connected), therefore, any tension in the body can effect certain areas of the body. Clenched fists, along with a clenched jaw can causes tension in the shoulders. Building upper body strength via strength training is important. Also, go through a check list every once in a while during your run...are my hands relaxed? Are my shoulders relaxed? Is my face/jaw relaxed? Am I maintaining an upright posture? If you answer no to any of these questions, then take some time to make some tweaks.
It's been 6 years since I started running and I still have a mental check list that I go through...especially when my long runs go longer and fatigue starts to set in. That is when we tend to allow our form to fall apart.
I hope this helps!