“I have an injury should I push through it or let it rest?”
First, go see a doctor. A doctor, I am not. If we are talking minor pain during our workouts we need to evaluate what we are doing. You need to decide if you are hurt or are you injured? If you are injured you need to see a physician before it gets worst.
If we are talking minor pain during our workout I still advise letting it rest. Unless you have a chronic injury that you are aware of working out should be asymptomatic or pain free. Exercise consists of repetitive movements and applied stress to the body. A great combination to turn “hurt” into “injured”.
Conclusion: See your doctor. If you are cleared to return to action start slow and monitor your pain. Not going to see a doctor? Give it some good old rest. Letting something rest for a couple weeks is better than being injured for a couple months when you can’t perform any exercises.