OP, there’s a lot of issues here.
First: like DancingArabian said, it sounds like you’ve got a lot of holes in your riding ability. I own an OTTB, and the very first thing everyone - including his trainer - told me was never, ever pull back on the reins, because a lot of them are trained to run faster when you pull back on the reins. So we spent the first six to eight months under saddle learning seat and leg cues. When he was solid on those, we began to teach him that a gentle pressure on the reins does not mean ‘run.’ Today, he’s a lovely solid Training Level dressage horse, but it took quite some time. And he was NOT my first horse. More like Horse #12.
I’ve met Thoroughbreds I wouldn’t dare ride, and I’ve met Thoroughbreds that are absolutely saints. Different bloodlines and different handling/training methods produce vastly different horses.
How do you regain your confidence? You need lessons, and lots of them. You need a riding instructor who knows OTTBs, and I hate to say it, but I’m not sure how much your instructor is teaching you. What do you mean when you say you’ve “fallen off plenty of times?”
And I’m sorry, I know you didn’t ask this, but I have to say it: you need to decide what it is you want to do with this mare, if you do decide to get her. A foal means you will lose a year in competition. Are you prepared to handle a foal from Day 1? To halter-break it? To teach it to clip and tie and load? Do you have space to wean him/her when the time comes? Do future plans include keeping and training it, or selling it? Do you have the money for unexpected vet bills? It’s not a thing to take lightly.