I would recommend you check our the barrel sticky on the forum. It's got great information for newbies to barrel racing. Barrel Racing Exercises and Drills.
As far as teeth, you will not be able to see anything just by "trying to look up there". A horse's teeth go very far back into the jaw and you need to have them sedated with a mouth speculum to see way back there. I'm glad you already have an appointment set up.
This is why I suspect your horse either 1) has a dental issue 2) has a training issue........ Her head skyrockets with rein pressure.
Are you working with a trainer? I think that would be the best thing you could do right now. We can try to help over the internet, but it is not the same as having someone help you in person; even if it is just a couple lessons. It doesn't even have to be a barrel trainer, because it looks like your horse needs to be softer in the bit. Period. Does he act that way other times? He is very much resisting any rein contact. You'll need to work on that AWAY from the barrel pattern first.
Going into the barrel turn, your horse's butt is already swinging out. This is your first barrel, from this angle I should only be able to see your horse's butt -- not a side view. Your horse also has no bend in her body. Her body is straight, but you are asking her to crank her neck around. This is making her very unbalanced.
This is how you should position yourself for the first barrel. Look at how much bend her horse's body has, look at how low she keeps her hands.
This is how your horse should actually turn the barrel. This is what I mean by your knee should be past before you ask your horse to turn.
No looking at the barrel!!!! If you look AT the barrel, your horse goes where you look. Do you want your horse to run OVER the barrel? No, of course not. So instead, pick spots on the ground around the barrel where you want your horse to travel (about 3 or 4 feet away from the barrel all the way around). Look at those spots instead.
Chicken arms alert.
Get those hands and arms down low!!
My riding is not perfect either, but I'll share anyway. Notice when I stop at the barrels going slow that I use my outside leg to ask my horse to step his hip inward. This is going to keep his butt IN and engaged for the turn.
I have my hands slightly elevated to keep his shoulder elevated, but my inside hand "lifts" higher than my outside support hand.
I'm using my inside leg to ask him to wrap around that leg and bend.
Look at how much space I leave him around the barrel when going slow. That will automatically suck in when you add speed in the future.
See how he's calm and relaxed and listening? It took a lot of training the last year (general riding) to get him that way.
Loping our first barrel needs some work yet, but I haven't worked the pattern much with him and he's coming along.