How can I convince my parents to let me get a bigger, softer bed?

I am 13 years old. I am a girl but I am super tall, 5 foot 8 inches and still growing. I also have severe scoliosis which makes my back hurt all the time. My twin brother has a full size bed and we are pretty much the same size. I haves double bed and we recently moved it, ( it use to have one side resting against the wall) and now both sides are open and I can't relax and stretch out because it's so small and uncomfortable. How could I convince them? It's also a matter of my back too.