I was eating something crunchy when I suddenly got jaw pain on the left side near my ear whenever I clench my teeth. Is this something I can wait out?

Be careful. You could have strained your left TMJ when you were eating. If the range of motion of your jaw is not affected and you experience no pain/discomfort or popping/clicking in the joint when you open and close and if you don't notice a change in your bite then you can expect it to get better. Just eat a softer diet, try taking an NSAID like advil (ibuprofen) and alternate between hot/cold compress on the joint.
TMD. If clenching causes pain in front of the ear, you may have temporo-mandibular disorder. The pain may be coming from the jaw joint, but more commonly from the muscles of mastication (muscles that close the jaw). See your dentist for a specific diagnosis.