Hi, Rachel,
I'm so sorry to hear you're having a bad time right now. Since you've only had tinnitus for a month, it's very possible that things will improve as time goes on. One thing you could consider doing is to get a prescription of prednisone from your doctor; some people whose tinnitus is new have had good luck with it helping or reducing their tinnitus.
Tinnitus is usually worse when you lie down to sleep, because there is nothing to distract you from the sound. Do you have an app you can play, or a sound machine, that has nature sounds on it? That would help mask the tinnitus, so that you could get some much-needed sleep.
That pressure you are feeling in your head is very common, especially in the early days of tinnitus. I had the feeling of fullness (or pressure) for quite awhile when mine first started, and it finally went away. I don't have it any more, but I remember how bothersome it was to have it all the time.
I don't know much about TMJ, but you could try going to a dentist or a TMJ specialist to have them check your jaw, and determine if that might be causing your tinnitus. Do you have any symptoms that are related to your jaw?
It's hard to say whether your tinnitus will go away on its own, or stay with you. However, if it does stay with you, the good news is that most people habituate to it after they've had it for awhile. They can still hear the sound, but it doesn't bother them any more. You can help yourself toward habituation by trying to live your life as normally as possible. Find ways to keep your mind distracted most of the time, and I believe you'll find that things will improve.
I'm sure other people on this forum will have additional suggestions for you. Stay calm, don't panic, and follow some of the suggestions on this forum. I'll bet things will begin to look better for you!
Best wishes and hugs,
Karen