Have you tried mounting, then dismounting, over and over again until you start feeling comfortable then riding (then repeat each time you ride and start phasing out the holder person, like mount once with the person, mount without the person, etc)? It'll be good practice for the horse you ride and it will most likely help you start feeling more comfortable.
I totally understand what you're going through though.
For me it's cantering. I'm terrified to canter. Once I actually am cantering I love love love it but if I don't know the horse or if I don't totally love the horse/feel safe on the horse I just can't do it. I was bucked into a barn door (I was bucked off other times by this horse but the door was the most mental and physically scarring incident), on to the hook part holding the door closed, at the canter (I have a scar on my back) and ever since then I just can't handle it. It's been about 4 years but I'm still working through it.
Finally I got a trainer that was sensitive to this issue of mine but she doesn't baby me about it. She asks me to canter during my lessons and if I do it that's great but if I just can't she tries to get me to have at least one canter step then I can stop and go back to my comfort zone. My pon-eh has been a big help in that respect too because she never ever gets out of control at the canter. I also have her trained to stop when I say "ho", so I feel a bit safer because I know can stop her completely no matter what.
I think in your case if you can't make yourself do it, you need to find someone who'll pretty much make you do it while not making you feel dumb for being scared. Being thrown into walls is not exactly my idea of fun either. Haha After you've done it a few times in an environment you feel comfortable in I can pretty much guarantee that you'll still have twinges of fear but that you'll be so much more confident about it.
For instance, a month or so ago I got on a pony that I hadn't ridden in over a year and was cantering him by the time I was done working with him for that session. I was terrified when I first asked him to canter but I kept going because, for me at least, the more times I stop doing something because of my fear, the more fearful I become.
Also, when I tell myself that I "can't" canter I really can't but if I say "I'm going to put on my big girl pants and canter and who cares if the horse bucks, I'll show it who's boss!" I find I get less scared. Getting POed about my fear helps me. Haha I also talk to myself when I get scared. I say things like "Are you kidding with me? I can handle this, I've ridden rearing horses more people are scared of those than bucking horses!" and "if I can ride through a rearing/bucking fit I can definitely hang on at the canter!" and "If this horse thinks it's going to pull any tricks, I've got my bases covered," you get the point. Lol I also tell myself yo' mama jokes (I just make them up on the fly so they don't really make sense but that makes it funnier!) when I get scared. For some reason I love them and it gets my mind off being scared. ROFL!
Good luck! I also find that if I focus on the positive future like how much fun I have when I canter, instead of what might happen if Lacey were to decide to buck, I do a lot better.
Sorry for the novel.