Typically, smaller horses (under 14 hands) aren't going to make it at the pro rodeos. However, there are always exceptions to the rule. Christy Loflin's mare Movin is only about 14.2 hands and they won the Pendleton RoundUp last year. (Go to 4:53 of the video to see her run).
And world champion Sherry Cervi's horse Stingray, I believe, it only about 14.2 hands as well. She excels on both big and small patterns.
Size isn't so much important as is the horse's physical ability, talent, and HEART. A horse that wants to do its job will excel; no matter the size.
From your description, your horse is probably around 13.2 hands or so. That's fairly small and I've never heard of THAT small of a horse doing well for the National Finals Rodeo. However, that's not everyone's goal. What are your goals? At what level do you want to be competitive?
You video is very poor and I can't see much from it. I do see that your mare is wringing her tail throughout the run. Sometimes that can be a sign that she is in pain. Does your saddle fit well? Has she been checked by a chiropractor? Has she had her teeth done by an equine dentist? Lameness check by a specialized vet? It is worth checking out, because if she actually is in pain (trying to tell you by wringing her tail) she may learn to resent the barrels because they "hurt" her.
How long have you been barrel racing on her? It looks like you need to take a step back and go back to slow work because she 1) is not rating 2) is not listening to your cues 3) completely blows the backside of the turn.
Lessons are never a bad idea. You can always learn something from another set of eyes watching you from the ground. However, make sure it is a reputable barrel trainer who does things RIGHT and doesn't cut corners simply to win. And hands-on training is always better than trying to get information off of the internet. We can explain things but its never as good as someone showing you in person.
But it never hurts to get your hands on every book and DVD you can find. And check out this thread we made for beginners: Barrel Racing Exercises and Drills.
Also, what seconds of time you get on your pattern means nothing to us. Every barrel pattern is going to be a slightly different size, and thus going to make a winning time have a different time. The only time you can compare barrel times to one another is when the runs have been made on a Standard Pattern.