My Jaw Clicks When I Open It And Sometimes Hurts. Should I See A Doctor?

Yes it is probably a good idea that you see your doctor, but also consider making an appointment with your dentist. The dentist will have a strong working knowledge of that are and can perhaps suggest some exercises which could release tension in your jaw.

Clicking could indicate a few things, including having hyper mobile joints. A lot of people have a 'clicky' jaw which doesn't bother them, but if it is causing you  pain that is not good. Pain could be caused by swelling and tension in the muscles which could also cause headaches, neck and shoulder pain.

If exercises don't help you may be referred to a facial surgeon or specialist to take a few x-rays or MRI scan to see the bone structure and any swelling or blockages which could be obstructing movement.

As with every ailment it is best to seek help sooner rather than later.

Yes.By symptom which you mentioned ,it looks to me a case of sublaxation of temporomandibular joint, for confirmation one has to go for investigations like plain x-ray,c.t scan etc.