One of the important things about working out is knowing which muscles you’re actually working out so that you can consciously focus on firing them off with force.
Pushups aren’t for your arms, at least not normal pushups. They work your triceps a bit, and a few of the stabilizer muscles in the forearms and shoulders. But, for the most part, push ups are about your chest. Squeezing your chest inwards should give you your upward momentum, not pushing away from the ground.
It’s also not quite enough to just have a straight back. You ever flex your stomach while looking at a mirror and it kind of auto-straightens your back? That’s the move you’re lookin for, tighten your abdominal muscles as best you can to make it so those are the muscles supporting your lower half, instead of pushing that weight onto your lower spinal column and shoulders