I agree with BarrelRacingLvr.
I would honestly forget about barrels right now, and simply work on getting your horse better broke and more responsive to your aids. If you can improve that, when you bring him back on the pattern, you'll progress MUCH more quickly.
That's excellent to hear that you've been taking is slow the last 6 months. Too many people rush through training too quickly.
Just curious, can you post a picture of what bit you are using on him?
And also just curious, how old is your horse?
As far as your picture:
--Your reins are too long. Your hand is nearly at your hip. Shorten them.
--Each horse horse will need a slight different rein cue, but I much prefer to "lift" up and in with my inside direct rein (so my inside hand lifts in the direction of my outside shoulder), to help keep the shoulder up. In your picture, you are almost pulling straight back and outward. I personally like to do something like this with my reins during a turn:
And ideally, if you've got good body control on your horse, you shouldn't need too much rein in the turn because they should be doing it automatically to some degree.
And I just want to say: YAY for another helmet wearer!!!
Looking at your video:
You need to give your horse more "warning". You got to the first barrel, and then you all of a sudden asked him to turn. And I do think you are pulling "down" too much with your rein cue. You don't want your hand to go that low. Keep your hands UP.
As you approach a barrel turn, you should be asking your horse to BEND. Nose in, ribcage out, hips in. Use your legs to accomplish this. He needs to have bend in his body when you arrive at the pocket, or he won't physically be able to make the turn.
Overall, you are just happening to randomly lope around 3 barrels. It doesn't look like your horse understands what is going on, and you don't have any precision. You should try to ride the exact same pattern and lines every single time. Follow these red lines:
And do that EVERY single time. Horses learn from consistency.
Is there a reason you take him to the left barrel first? Nothing wrong with that, but just curious why you have chosen that direction.
So when you head to your 3rd barrel, do you see how you head WAY wide to it, cut the backside tight, and then come out WAY wide? Instead, look at my drawing above. Head directly for your pocket point. And do not start to turn until your knee is AT or PAST the barrel. And then make sure you finish the turn tight.
Work alot (in general) on controlling your horse's body. Be able to move his shoulders, ribcage, and hips all independently of each other, using your body and legs. Do lots of circles, figure 8's, and spirals to learn how to control every step and every piece of his body. You want to be able to place his body wherever you want it, at any time. You need this precision in order to make split-second adjustments when you run a barrel pattern. Of course, you have to teach this slowly in the beginning so that you rhorse is broke, broke, broke.
Check out this sticky we made for beginners: Barrel Racing Exercises and Drills.
I noticed your horse swishes his tail a lot. While some horses just plain do that, it could also be a sign of discomfort.
--When have his teeth been looked at last?
--Does your saddle fit?
--Has he been checked by a chiro or vet?