What could be a reason why my jaw hurts on the left side at my temple when opwning my mouth an tender to touch an is swollen i've had recent tooth ext?

Soreness: Probably soreness from the tooth extraction. Taking a tooth out causes some trauma to the area. I suspect that all of this will clear up completely in a couple of weeks. If it does not feel somewhat better after one week you may want to check with the dentist that removed your tooth.

ROOT FRACTURE: It's possible a root fragment is left in socket or infection is still present have a post op. Xray taken by your dentist.