Be prepared for dumb questions. Please forgive me.

I've been riding my SS to school every day. It's geared 48/18, and I can spin out pretty well on flat ground and downhill. It's hard to describe, but when I'm spinning out it seems like the harder I try to pedal faster, the less I can do. Is there some secret technique I'm missing, or do I just need to continue? After spinning as hard and as fast as I can for a while my legs ache all the way from my feet to my hips. Am I doing it wrong? Is there anything I can do to improve?

Thanks

Edit: I should add that I've only been riding FG/SS for a few months, and I've never realized the value of spinning before.