Maybe you need to have a talk with your instructor to let her/him know that you are afraid. It may be as simple as your sturrups need adjusted or your saddle may be too big for you.
Are you riding english? If so you may need to get some breeches with a full seat. If western maybe you need a rough out seat. I ride western with a rough out seat and full seat breeches so I am really glued to the saddle,
It really helps to keep your butt from slipping out of the saddle.
Another suggestion is getting an exercise ball for doing some balancing exercises at home.
Its tough to get that courage to go fast and gaining the trust in a horse to not hurt you. It will come in time, and don't be afraid to talk to your instructor about your anxietys. As John Wayne said "courage is being scared to death and saddling up anyway"