Horses do this all the time, don't worry.
I assume based on the description, the boots were splint boots - Maybe like these?
I don't really use splint boots just because I like sport boots better, but they shouldn't rub like that regardless. Maybe there was already a scab and it just pulled it off?
I will recommend to you maybe getting some sport boots. These are my favorite - 7arrowsfarm
(She also sponsors me so I feel like I should leave her link, though any Iconoclast boots from anyone are good.)
Even though they are a little spendy, they are worth it for the support I think. They will also protect against scrapes and such. Along with those maybe get some bell boots, or overreach boots (Also seen on that page). I'm a bit of a boot freak, I always ride with them because I've had a lot of times when I go to work that a horse comes out injured from hitting itself or something. Not an issue at your level of riding right now, but maybe in the future, and it will give you peace of mind until then.
Agreed also to talk to your farrier. Is your farrier a member of the AFA? If not I would look up one who is on here. AMERICAN FARRIER?S ASSOCIATION
Not to say a farrier can't be good when they aren't certified, but....They generally aren't good unless they are certified. If there isn't one in your area take what you can get and stick with who you are using, but if there is, I'd call and try to get on the books because even though it's a few extra bucks it's SO worth it not to have any trouble, to have someone who can diagnose problems, and to have someone do a good job so you don't loose shoes every other day. Quality is the difference between a 60$ shoe job and a $100 shoe job! (Or trim.) I have participated in a lot of their competitions and certifications, these guys are the real deal - I would let even the rookies work on any of my horses.