Yes. What most likely happened is that you strained muscles in your upper and/or mid back. When this happens you essentially are pinching nerves; this is where the pain sensation comes from.
Through the muscles run nerves and when you irritate a mucle it gets inflammed and taut. This intern will create pressure on nerves. I've done the exact same thing before. For push ups you flex your chest muscles but your rhomboids and thoracic paraspinals elongate or stretch so you can stress them too. Also if you are curling even light weights you will use your biceps but when they fatigue you'll hit the back too. Use something to
massage this area of your back.
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