could be carpal tunnel syndrome. When your wrists, etc are in the same positions all the time, you'll have numbness, and pain. Maybe you don't get it on the acoustic because it's bigger and of course you have to hold it differently. Do you stretch your hands, especially the fretting hand AFTER playing? Not so much before as your hands aren't warmed up, stretching cold will hurt you! I stretch the wrist up, down, and sideways, it's a ritual for me! Sometimes my fretting wrist and forearm will be tight if I've played too much, and by slowly and gently using my right hand to push my left thru each stretch, and by the finish, I won't feel the tightness that I had!

Also like the other said, about straps, I use my cross-back strap EVERY time I play, sitting or standing, it centers the guitar on my chest and I don't have to hold it, just play it! You should borrow (or buy cheap) another electric, see if it hurts you also. I've only played electrics and each one felt different, so if it's that electric only making you hurt, you need to change it to another one!