Migrain? Tension Headache? Terrible Head Pain

For over 2 years I have suffered from terrible headaches. There was no particular trigger that I can think of that began this concurring issue, just waking up one day and never really having it permanently  leave. My symptoms are as follows:-

1. Terrible head pain. The funny thing is, it never stays in one spot for too long. Sometimes I feel it in the back of my skull. At others on the top of my head. Still it will shift from left temple to my forehead. My jaws sometimes get tight, but no clicking noises on opening or closing them.

2. Sometimes lightheadedness comes with these headaches. Not always. Its more like a brain fog after waking up from a nap.

3. Sometimes I wake up with the headaches, other days I wake up feeling great for about 30 minutes.

4. Sometimes there is relief from getting up and moving around. Sometimes moving makes it worse or triggers it. It shows up with rest, or sometimes with physical activity.

There is no great pattern to this. Sometimes doing an action such as going for a jog will take away all the pain and I feel great, and other days it just is too unbearable to exercise. Pain meds don't really do a whole lot in terms of helping me. I have had CAT scans, blood work, PT, and so much more. I really have no idea where to even go from here. The headaches aren't always present, more like 80% of my day. I work out 6 days a week, even if the pain is there or not. It wasn't always that way, the first year of my headaches I didn't want to do anything and gained some unwanted weight, but I came to the conclusion that I can be fat with headaches or in shape with headaches. I work in the military, so half my day is at a computer and the other half is pretty physical. I am 33, male, 5'7" 155 pounds. I love life and would not call myself a victim of depression, although this headache stuff is getting pretty annoying.