Sore vs. pained muscle

I'm quite sure I know the difference between sore and pained, but is it possible to pull or strain a muscle in one arm and not the other using the same size dumbbells?

I was only using 8 pounds on either arm and doing one legged bicep curls as well as bicep curls on the stability ball 2 days ago and my right arm, if I let it drop to my side, is in pain, not horrible pain, but pain, whereas my left arm isn't really even sore anymore(was yesterday a little). If i raise my right arm above my head, nothing, no pain, no sore, but if I let it drop to my side or push it out behind me, it hurts...like I said, it's not unbearable but it's pain nonetheless.

I was on my way to the gym now, should I push through it or let it rest?