There is a young lady at our barn that has to work off her lessons at the barn by cleaning stalls. She just recently bought this incredible 5 year old paint and I asked how she did it. She saved her birthday and Christmas money, and offered to ride or lunge boarder's horses when they couldn't get out to give their horse exercise. Now that she's bought the horse, she's trying to earn money to buy a saddle, so she's doing the same thing. As boarders go on vacation, they hire her to exercise their horse a few times a week, or when one set of parents bought a horse that was way too much for their daughter, she rode him for $30 a session to try to tone him down a bit. She now has almost enough money to get one of the nicer saddles at a local pawn shop (quite reasonably priced I might add).
Now, she's extremely talented and everyone at the barn trusts her with their horse. I would put her on any horse out there--she could handle it. If you have a reputation like her at your barn, why don't you offer to exercise horses for people who can't get out to the barn enough. It's given her a lot of experience. She just recently had shoes put on her horse and she told me that she offered the BO's husband a day plowing arenas and mowing if he taught her how to drive the tractor so that she could earn enough to pay for the shoes.
If you are resourceful, you would be amazed at what you can do. My 8 year old earned enough to buy a new saddle pad and reins by helping out. She told my husband and I, and my parents that she wanted these things for the horse, and she wanted to know what she could do around our houses to earn the money. My dad paid her a quarter a pine cone at his house which worked out to be about $15! Be upfront with people when you are asking for work, even your parents. Tell them that you'd like to earn some money for shows, and make an agreement about how much you will earn, and do your job well. People will want to continue to hire you if you do a good job.
As a high school teacher, I find kids who are willing to work for what they want to be most successful in life. I commend you for trying to find a way to do this yourself. You'll value it a lot more this way.