I totally know that feeling! *hugs*
What helped me, basically, was Lacey. Obviously you can't have Lacey (heehee) but I'll try to put into words what happened with her that helped me...
At first she scared me silly, I would get on and my thoughts would start racing: "what if she spooks?" "what if she rears and goes over?" "what if she bolts?", those sorts of things. After riding her for a month or so, I realized that if I emptied my brain of thoughts and only focused on the task at hand, she would behave much better. She stopped breathing like a freight train and she stopped spooking/bolting/rearing nearly as much as she had been. But it took me longer to figure out the perfect "formula" to empty my brain. I think it's probably different for everyone but for me it's not too difficult. If I start feeling myself tense up or if I feel my thoughts start going a mile a minute, I kind of collect all my unnecessary thoughts and push them out my legs (which also helps me lengthen my legs out and get in a more functional riding position), then I roll my shoulders and loosen all my joints and limbs-when my mind starts racing I tense up, then, perhaps the most important bit is that I sigh out loud. The sighing for me is very important because in my mind I'm releasing all that pent up energy, all that "dirty air." I'll repeat that as many times as necessary until I'm staying calm and collected without thinking about it. Now that I've been doing that for so long I can do it with just an out loud sigh, but to begin with it was a process.
Another thing that has helped me get over my fear is getting "mad." I don't really literally get mad but I get fake mad. I pretend to be mad about this horse taking advantage of me (cantering before I say to, trying to leave the arena before I say so, etc) and that gives me the extra oomph I need to get that horses attention and correct it. I tell myself "look at that horse! He/she is walking ALL over you, that's just not right!" and then I get very decisive and I stop being Little Miss Nice Gentle Cues. I stop trying to be gentle and I turn up the heat. Each wrong move is reprimanded quickly and efficiently and I don't take no for an answer. As my trainer says to kids who've never ridden before: "do you have a older brother or sister? You know how they boss you around? Well you need to boss this horse around, he/she is just like your little brother or sister." That's probably a little oversimplified but it's kinda the right idea.
Usually, the first method works best by itself on more sensitive horses that are reacting to the world and need you to be calm so they stay calm, and it's great to use to calm yourself before you use the second technique with horses that are just trying to get away with being jerks.
Also, as a hopeful thought for you, I am very timid by nature and a few years ago I had some really bad experiences with cantering. Since I am timid, I was then put off of cantering in a big way. I would consider cantering and my palms would get sweaty, my heart would start racing, and I'd feel like I was about to barf. Cantering unknown horses that I didn't know/feel completely comfortable with especially terrified me. But I've been slowing working on it, trying to canter more, using those techniques, riding more different horses, and yknow what I did the other day in my lesson? I hopped on a horse that I've only ridden around 5 times (and do not like, at all), my instructor told me to canter, and yknow what I did? I cued that horse to canter! I didn't get sweaty, I didn't start freaking out, it was no big deal!
So don't worry, you can become less timid of a rider if you really work at it, it is possible!
Also, I would definitely tell your instructor that you have those issues and see if he/she can give you tips or help you feel more secure.
For instance, with my cantering thing, both of my instructors know of my fear. The one that owns the barn Lacey stays at never pushed me to canter. She'd ask if I felt comfortable cantering and if I felt ok about it, we'd try. She never asked me to canter when I didn't feel comfortable and she didn't care if I chicken out asking the horse to canter or if I only got one stride of canter before needing to stop. My second instructor (the one I've been taking "lessons" from lately) only puts me on horses that are completely dead headed about cantering. He doesn't let me get into a situation to be scared. He just gets me up on that horse and says "canter" and I do because I trust his judgment and because I know he knows that I'm scared. Both instructors have different ways of going about taking care of my fear but both of them have helped me.
Of course, I have no fear of cantering Lacey but that's just cuz I know her so well.
Sorry for the novel! Hopefully some of this babble has helped you a little! Haha
I totally understand what it's like to be really scared of something that you feel a little silly about. I also think it takes a strong person to confront their fear and take care of it, like you're endeavoring to do. =)