So I went for a "lesson" on Cowboy Mounted Shooting yesterday. This was our first time doing it but feel free to critique or give advice on what you see! I'm so excited to do more! https://www.youtube.com/watch?v=QZcmxybABkc
Since you asked, I will throw my belated two cents in...
Overall, you looked very good. First advice I would give is to follow the instructions you were given in the lesson. :)
The horse looked very good for a first-timer. There may be some potential there. Take it slow.
The first few shots caused the horse to speed up a bit. You want the horse to be going at _your_ speed, not his. I see a lot of new people get into trouble due to the "escalation factor." If the horse is at a trot and gets excited, he goes to the canter. At that point, you need to break back down to the trot, regain control and get the horse calm before taking the next shot. If the horse gets excited and you go the the canter, the next shot could cause the horse to get more excited and even more out of control.
While speed is eventually the point, remember that "smooth" is better. Doing it "right" and at an even, controlled pace is more important. You can always add "fast" later.
On the rundown, the horse seemed to be speeding up and you were pulling on the reins to keep him in check. I would suggest you work to slow down and try to do that rundown at a controlled trot while keeping a looser rein. That might be why he was starting to throw his head a little near the end. Keep the shot behind you.
I couldn't see all of the shots that well, but it seems you were doing this most of the time. Imagine straight ahead is 12 o'clock, directly to your side is 3 o'clock and straight back is 6 o'clock. You want to keep your shots at 3 o'clock or greater (i.e. 4-5 o'clock).
This serves two purposes. First, it keeps the noise and flash away from the horse's face. Less to scare him until he gets used to it. Second, having the noise behind the horse helps to move hie forward. You always want forward motion when shooting. I could be wrong, but I think that some of the horse's agitation at the first few shots may have been due to having a shot in front of 3 o'clock. Most riders have a tendency to shoot early, especially on the off-side shots where it is harder to keep the shot behind.
Again, looking very good for a first time out.
The only other thing I will mention is something that it may be too late for. Be careful the "next" time you try this on your horse.
Some horses do fairly well the first time. After they have a chance to "think it over" they decide that maybe it wasn't so fun after all. The next time you mount up and the see the balloons and guns, they remember. Then they give a little more attitude to try and get out of the work. This isn't true of all horses - but it does happen.
Also keep in mind that it takes a while to really train a horse for mounted shooting. Take your time and remember there are no shortcuts. Don't try to do too much to fast.
Hope this helps. Be safe.