Lancemanion - Never play through pain. You'll end up with problems later down the track. I recently had to drop my performance degree due to chronic RSI, which I never thought could happen to me. DON'T DO IT.
I've just started uke but had the same problems as you - does your neck strap support the neck of the ukulele? At first I had strap buttons put in at the base of the uke and also the heel of the neck, but this did practically nothing as I still had to support the instrument with my hands, esp the left hand... try tying your strap around the headstock if possible.
If you're in pain you're doing something wrong - stop and re-evaluate.