Afraid to canter what should I do

My first time cantering was unexpected and has left me rattled over the last month. I was doing a bareback lesson on a lesson horse I'd ridden multiple times bareback, and we were doing trot work when she picked up the pace and broke into canter. I couldn't get her to slow down through the reins or verbal commands and did my best to stay on until my trainer could get to her and help. I almost fell off, and I haven't had a lesson with that horse since.

I have ridden two other lesson horses since then, and I'm okay in the walk and mostly in the trot, but anytime they pick up the trot to their working trot I get scared, especially when this one lesson horse does a weird skip during the trot. That same lesson horse who does the skip has also tried to do canter steps while trotting in my last few lessons and it terrifies me every time. What if I can't communicate that I want them to slow down again? What if they ignore my halt aids?

I want to learn to canter because I want to be able to handle the faster gaits safely and be a good rider, but I don't know how to get there. I've only had one lesson where my instructor had me on the lunge line and specifically asked the horse to canter so I could attempt the faster gait, but we haven't worked on it since then. I know that riding horses is dangerous and there will always be accidents and that it's a when not if, I've always known this. I just don't know how to get over this fear so I can relax and grow as a rider. I also don't know how to explain to my instructor that I would really like to work on canter on a lunge line.

Last year I told them in fall that I really wanted to work up to cantering in the next year. They seemed very supportive about it, but it doesn't seem like much has changed in our lessons. I still work on balance and relaxing my upper body and different levels of contact. I've been riding for five years now, and everywhere I look people tell me I should be cantering already or it only took them a few months into lessons to get to that stage. I just feel stuck.

Any advice?