When I attempt to do this exercise with 8lbs, I can barely lift my right arm, and my right deltoid actually hurts.
I can lift my left arm easily.
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You really should get checked out by a medical professional to make sure you don't have something seriously wrong that you can't work through. Since it's your shoulders, I would imagine the odds are good that you have a rotator cuff problem.
If you can work through it, I'd start doing full range of motion exercises with weights that make it stiff feeling, but stopping well short of pain. The whole "good vs bad pain" thing really is legitimate. Every athlete works through injuries and random problems. The key is that you want to help your body heal and get back to a strong, full range of motion.
Often, a precursor to shoulder injuries is bad shoulder development: isolation exercises, bench pressing, lack of back strength, tight chest, and loose back. Not only do you want to fix things safely, but you want to minimize the chances of having a problem like this again in the future.