So my left arm cramps up when I play fast for a long period of time.

Is this just a "it will devolop by itself" thing or a "you are playing wrong" thing?
I think you're probably tensing up without realising it.

Put your hand in guitar playing position, without a guitar.
Move your fingers in similar patterns to ones you would play.
Now i don't know about you, but i can do this really fast all day and it doesn't cramp me, but when i do it on guitar it does cramp me. The reason is probably because i'm gripping and pressing too tightly.