Arm cramping up quickly means you playing inefficiently, you tensing your left arm is probably a bad habit you got when doing hard songs,. U said your right arm was fine so, copy what your right arm feels like, and do the same on your left arm which should fix that.
RELAXING:
Relaxing means that you use only those muscles that are needed to play. So, you can be working as hard as you want, and be relaxed. Relaxing does not mean to “let go of all muscles”; it means that the unnecessary ones are relaxed even when the necessary ones are working full tilt.
One way to feel relaxation is to start practicing from easier songs and increase the difficulty it until you notice that habit kicking in, then just relax tht arm.