I'll try and work through this bit by bit so bear with me.
Riding lessons at good schools are expensive, and cheap ones are nearly always cheap for a reason. Cheap lessons, particularly for a beginner, are a waste of money as the chances are the instruction will be of a low standard on horses who may well be unsuitable or not really up to the workload. They may be operating in a way that invalidates their insurance, which while you hope never to need is still important.
Which brings me to the next point of working for your lessons. Good schools will have enough employed staff so don't need helpers, plus the chances are you wouldn't be covered by that all important insurance. So a school that would take you as an unpaid and uninsured helper is unlikely to be a good school. Also, and no offence intended, but you don't know enough to be helpful and from a school's point of view it would cost them more than it's worth to teach you and get you up to speed. If they're willing to take inexperienced helpers and have them work unsupervised then run for the hills!
If your parents are worried about riding taking away from your studying then they're almost certainly going to seeworking all day for a lesson as a waste of studying time.
What other job were you thinking of? At 15 I really would recommend keeping your options open, and equine college isn't going to do that. I don't know what you think a RI's job includes, what the qualifications involve and what the wages are but the reality is long hours that involve more than teaching for poor pay and often poor working conditions. Honestly you' do better to study for a bit longer to get a good job then learn to ride and get a nice horse of your own that you can enjoy. Talk to career staff at your school and look into other jobs, there must be more than one career that plays to your strengths and interests! Planning your whole working life on one pony xperience day feels rather foolish to me, it certainly isn't a realistic taste of working with horses or even of riding and owning one.