Is he an OTTB? Has he ever been trained to be a regular riding horse?
I mention this because most OTTBs I know think contact=GO! And need patient, gentle restarting. You essentially need to teach them how to ride all over again.
His head is quite high and I wouldn't completely rule out saddle/back issues. You should have them both checked.
Once pain issues are rules out here's what I'd do:
I'd start all over, like he'd never had a rider on him. On the ground with his bridle on, apply gentle pressure to 1 rein with your hand rested on his withers. I do this so that the moment they turn their head they relieve their own pressure and the handler isn't tempted to keep pulling to get them to turn more. Hold the pressure until he turns even in inch in the correct direction, relieve all pressure and give him a rub. Rinse and repeat this until just a tiny ounce of pressure gets him to turn his nose to his stirrup easily. Steer him in both directions with you standing on either side, even turning his head away from you. I would do this with a regular nose band, not a flash - as he shouldn't need one at this level. At this point he'll learn that gaping his mouth or fussing won't relieve the pressure, but turning his head will. Mouth gaping (the reason we use flash nosebands) is mostly caused by a horse who's being nagged with too much contact (OTTBs) who have learned the only way to find any relief is by gaping their mouth. It's useful again when used properly in upper levels of dressage - but he's not at that point and should NOT need one.
Next I would practice this same giving to the bit while sitting on his back at a stand still.
Now I'd take him out for just a walk
around the arena, never, ever finish a lap around the ring without doing at least 3 things, any 3 things anywhere. But put in circles, changes of directions, cut the ring, start a figure 8 but then go down the center line. Mix it up! Keep him guessing. Mix it up between a heavy working walk to a long, low relaxed trot - practice stretching him down into the bit at the walk and pick him up again into some forward high action walk. Again, keep mixing it up.
Do this for a few days or even weeks, really get him supple and listening gently. Remember steering isn't done all with your hands - use your whole body to steer him, start with your eyes, shoulders, waist, hips, legs, then hands
Once you've been doing really well with this and have some good quality feel for a few days consistently, now add short trots. Change it up continually, again don't finish a lap around the ring without at least 3 things happening, now even changes of speed. In your short trots ask him to stretch low and deep into the bit using your whole body to guide him. Give him the rein he needs to do it. Keep the trots slow and relaxed at first, even if you need to use sitting trot to help keep him low and relaxed at the trot - remember to BREATHE!! I make my students sing their ABCs when they sit trot so I know they're breathing ;)
Don't trot more than a few steps at a time at first, this will help encourage him to relax into it, he's not going for an hour long trot, just a relaxed jog for a short while.
Gradually increase the amount of trot work and work on changing things up constantly. Pick up trots half way through circles, sometimes make circles toward the wall of the arena rather than away (this always throws them for a loop :P) Any time he gets worked up in the trot just bring him back down and relax him.
Eventually you can work on developing control over a good working trot and a soft relaxed jog.
Keep practicing these skills until they're solid - don't even bother with the canter until he's an ace at everything else, that's only reminding him to do the wrong thing.
Good luck, let me know if you need anything cleared up
ETA: just saw Kayty's posts, completely agree with all of it.
I also just looking at the picture realize I think you're hands are a bit high, based on the direction the reins are going. High hands= a high head. Remember to keep your hands low and slightly restrictive, but not hauling on his mouth as they appear in the photo. The video I honestly couldn't tell much from other than it doesn't look like a serious pain issue on the horse's behalf.