Hi Rachel,
I'm really sorry this is happening to you. When you say they gave you "migraine meds" do you mean preventatives like anti-seizure meds (Topomax, Gabapentin), beta blockers, or anti-depressants (Amitriptyline, Nortriptyline), OR do you mean abortives like triptans (Maxalt, Imitrex, Naratriptan, Sumatriptan, etc) and DHE? Or have you tried both? If you tried meds in the first category, how long did you stay on them? It can take up to three months to see an effect, and sometimes you have to use them in combination.
How many times per week do you take any sort of pain reliever or triptan? Could part of this be medication overuse headache MOH?
I have a bunch of different things that contribute to me being a STAR migraine disease candidate (ha) and like you, one of them is that I've had screwed up TMJ issues since I was a kid. I'm sure you already do like I do and don't ever eat anything you have to chew hard (I get a headache even from trying to bite a carrot.) Botox REALLY helps me in that regard because it puts key nerves in your head and shoulders to sleep for three months at a time, and I have a lot less pain for my good weeks after that.
For some people, nerve blocks (injections of steriods and/or lidocaine) are helpful. They don't help me, but some swear by them.
But there are also lots of things you can try at home to make your living space as migraine friendly as it can be. Have you looked at some of the migraine elimination diets posted here by Kerrie Smyres? I know my body is very reactive to food triggers. If I eat a food trigger, I have constant headaches for days. We make all my food from scratch at home. I eat almost nothing preprepared.
I would also check to see if you could be sensitive to light or sound. Try taking a break from lights and screens for a day and just use natural light from the windows. Does your head feel better? Some bulbs are better for migraine brains than others. They make special LED bulbs that some people tolerate well, and one of my neuro-opths recommends incandescents as the least irritating if you're really light sensitive.
Sleep disruption can be a huge trigger. Do you sleep the same amount every night? Do you get at least 7-8 hours of good sleep? My neuro reminds me that this is when the body produces chemicals that lower your trigger threshold. If you miss that production period, you'll be in trouble the next day.
Hope that helps. Sorry for the long response.