Lexie, your heart is in the right place but you can only do so much. You're 16.
Your mom must think the horse is pretty special to you, and, because you're very special to her, she'll gladly sacrifice her happiness for yours....because that's what a lot of loving mothers do.
Just the fact that you realize that it might become a problem for your mother does my heart good. It means you're becoming an adult and able to rationalize that the world is larger than yourself. Congratulation, you're growing up.
So, you're torn between your happiness, or your mothers well being in old age and retirement. Again, that's good....really good....now, you have to find your own solution. Do the math...write down the expenses and be honest with your mother. She might be able to do it but how much of a problem will it become for her if it goes on for a prolonged period of time? Can you live with yourself if it becomes a problem for her?
Maybe this abscess an such is a temporary situation that only need to be treated for a month or so? What's the long term prognosis for the horse? I mean, my horse is barefooted and abscessed a few years back but in a month or 6 weeks she was fine and hasn't never had another foot problem.
Did you ever consider that you might just be your mothers retirement plan? I mean, when she's not able to work are you going to care and provide for her like she has for you?
You're thinking about the right things....that's a good start.