I havent read any of the other replies so I apologise if I repeat anything.
Fear is natural...its even normal. If we werent afraid we would have no concept of what could happen to us. Just like when you are really young...you have no idea what could happen therefore you don't have a fear. You can't have a fear of something you don't comprehend. If you don't have a HEALTHY fear then you are in for trouble.
Having said that, we need to learn to put that fear in a place where it doesnt interfere with our daily lives. Fear can be so crippling and it can stop us from doing the things we would really love to do. For example, I would looooove to go skydiving but I am so terribly afraid of heights that I can't even do the short training and do a tandem skydive. Its stopped me my whole life from experiencing the feeling of free falling from the sky. And, its something I don't think I could ever get over. But, jumping out of the sky at 10000ft is a little different I know.
When we get scared on the back of a horse its because we truly truly understand what we are dealing with. Geez, a horse or a fall could kill us in a second. But knowing what can hurt us and understanding it are two different things. Sure you have a fear of what MIGHT happen but do you have an understanding of why a horse would do something that would make us fall of or hurt ourselves??
Next thing I want to say is about your own confidence. So many times I've seen people not get where they could because they let their fear get the better of them. You said your trainer knows you can jump 2'...listen to her!!! Your trainer can see what you can't and she obviously sees that you are capable of doing more. When you get afraid of something its sometimes hard to see clearly what the situation is. Trust your trainer and yourself, its the only way you will learn to push yourself past that point of fear so you can recognise exactly what you can do.
Also I would like to say that it would be good for you to be constantly riding the same horse. Once you get to know a horse and trust a horse you can find yourself doing things you normally wouldnt when you are riding a horse you don't know. I know sometimes its hard depending on your situation but knowing the horse you are riding can get you a long way.
And finally, im sure you are not alone when it comes to having a fear of galloping. Galloping is the fastest and most unpredictable speed and if you have a buster at a gallop it will certainly hurt more than at a trot or canter but by choosing the time when you decide to gallop you can more easily avoid any problems from yourself or your horse. Please don't try galloping or jumping higher though until you have settled in your fears and are more ready to face riding with a sense of fear yes but not a fear that is going to take you over. Remember, your horse can tell if you are scared and this is going to make the situation even worse
Good luck and I hope my short story has helped you a little lol