I am glad all seems ok now. Do make sure your parents understand the legal obligation they have to your guinea pigs. You are not responsible for your animals if you are under 16 - even though you do all the caring for them, you are a minor and your parents are responsible for ensuring their care and ensuring all their needs are met, including medical needs. You rely on your parents, which means your guinea pigs rely on your parents - unfortunately without their support you are in a very difficult position.
Even though it all turned out ok this time, please make sure your parents are aware of this in case one of your pigs does become ill.
I have been there myself, although my parents have never outright refused to take one of my guineas to the vet. I only rely on them to drive me now, I do all the care and paying for everything myself. Although I do rely on them to keep a roof over our heads too!