While aero bars might be a remedy, I'd say that you should look VERY closely at your bike fit. If your palms are hurting, you're not moving your hands around enough or are stretched, too much drop, too wide bars/etc. Something is "too much". That something could also be a weak core.

100 miles on the tandem, my palms/shoulders don't even feel like I rode. Be it my single or tandem.

Also, you can look at your gloves, they might be pinching or bunching in the palms.