Don’t get upset with the BM about the lack of pay-- I know you probably won’t see it this way, but that was entirely your choice to keep working there even though she wasn’t paying you (or paying you enough). I’m sympathetic because as a young person it’s really hard to stand up to adults, and this BM seems to have taken advantage of that. But regardless, lesson learned, right? You’re close to being out there on your own at college, etc, so be glad that you’ve learned this now, without huge consequences.
Bottom line, I think this boils down to your belief that you should have more flexibility in what days/hours you work, since you’re not being paid. And it turns out, the BM disagreed. She may have her own reasons that seem equally valid to her. No big whoop, this job just isn’t a good fit for either of you anymore.
For your next job, you’ve learned some great lessons, especially about needing to define the compensation expectations more clearly. And scheduling time off needs to be done well in advance–whether or not you are being paid. The boss has no obligation to tell you their travel plans in advance. If you’re scheduled to work, they have every right toy assume you’re going to be there to do the work, and make their own plans accordingly.
The burden is on you to understand how far out vacation / time off needs to be planned, and honor that rule. Sounds like in this case at the barn, you didn’t have a clear sense of how far out you needed to alert the BM, so you surprised her with the college tour on short notice. [ETA: just saw OP’s last post. Sounds like enough advance notice was given]
As for the sick time, here’s a hard truth: Excessive sick time will cause you to lose your job, no matter where you work. It’s not fair, but no place of work can function very well when its employees don’t show up (no matter how valid their symptoms!!). Make sure your parents know how bad your migraines are and ask to see a doctor. Hopefully you can get some treatment options. I used to get them when I was young like you, and I know how awful they are. The good news is I learned that they often were caused by dehydration, stress, and other things that I could control, so I was able to bring the migraines under control. I really hope you can too. I know they’re awful.
ETA2 --OP, bottom line, it doesn’t matter how “right” you are. The BM is not going to care very much, and after a week you won’t even think of that barn. Just give notice and move on to your next adventure.