Originally Posted by DannoXYZ

Don't push so hard. Pick easier gears and spin your legs like hamsters. Your upper-body is sore because it has to combat the rocking motion of your upper-body due to the heavy pushing from the legs that throws you back and forth. By pushing lighter on the pedals and spinning faster, you won't need to counteract the leg forces as much with your arms & shoulders. You shouldn't ever feel any force on the pedals at all, rather your legs should feel like you're a hamster on one of those spinning wheels; about to fall off...