Hi,
How are you? Are there other symptoms present? Temporomandibular Joint (TMJ) headaches is indeed one differential and may present with a muscle-contraction type of pain. It can also be accompanied by a painful "clicking" sound on opening the jaw which is caused by malocclusion (poor bite), stress, and jaw clenching. Check with your dentist or doctor about this for proper evaluation. Take care and regards.
Regarding left jaw and neck- you'll want to make sure you don't have a heart issue, as pain can refer to these areas from the heart. And you may want to get a doppler of your carotid, to make sure it is fully patent.
Also, you might go to a dentist specializing in TMJ disorders or a maxillofacial specialist, because a problem with the jaw is strongly suspect with headache on the side with jaw pain. Do you clench or grind your teeth when you sleep? I'm a clencher myself and I have both joints with arthritis and joint disc dislocations, with one of them out of place even when I open my mouth (called without reduction, I believe). I wear a hard flat planed splint that helps quite a bit with the intensity of the headaches, I believe, as the last time I went one night without it, I got an extremely bad migraine.
Also, with the word "pressure" I think of sinus headache and you might want to see an ear, nose and throat specialist if you think this could be an issue for you.