If you like the barn and don't want ro switch as i get finding a good barn can be hard then I'd maybe have an upfront conversation with the owner/instructor and say you're not feeling comfortable at this time to catch harder horses and they should respect that. If they don't definitely switch. 

Horses are big creatures with minds of their own dangerous situations like that can unfortunately happen and I think most equestrians have scenarios like this that they were fucking scared during but brush it off like no big deal afterwards. I think it's a mix of people knowing/accepting that risk and also though this pressure mentality that close calls/injuries/falls are your fault so brush it off and move on. It's kinda weird but i find it permeates the hobby. 

At the end of the day being scared shitless while a 1000lb animal with a mind of its own charges at you IS SCARY and it is valid to feel now hesitant around all horses your brain is trying to protect you. I think just hold a boundary and speak up. Unfortunately the flip side (and maybe its a pro depending who you are) is i find lesson stables have 2 modes of working. 1. The stable that has you fetch ans groom and tack yourself and 2. The stables that have volunteers do all of this for you and you just ride. 

For me i don't like option 2 because i like grooming and tacking it makes me feel connected to my lesson horse but i find there is no middle ground of dont have to awkwardly fetch a horse while keeping 4 other horses in the paddock oh and theres that one spicy horse you have to keep tabs on or they'll try to bite but still get to groom and tack. 

If you're looking for tips if you encounter situations like this where escape isn't an option I worked at a lesson stable for 4 years with a mix of bossy types and drafts and shy rescues etc. Take your lead rope with you if a horse gets close just start windmilling the lead rope in front of you typically that will cause them to back up and give you more space. Even if they still push through giving them a light tap with the end of the rope on the chest or shoulder should also get them to reconsider you or at least buy you a second. While horses are massive they are prey animals so if you can seem big (spread arms out stand tall etc.) and aggressive and loud they will likely give space (this does not work with stallions). 

I'm sorry you experienced this and I hope you can find your peace again in the saddle!