Bigger grips, some thin but grippy gloves and relax your grip as much as possible (thin grippy gloves to maintain feel and grip). Also get one of those straps that presses on the muscle just below your elbow.
You could even try wrapping some bar tape around your grips for now to see if it helps. I use ODI Rogues, not found a bigger, grippier grip yet.
I also change hand position a lot including holding onto my brake lever reservoir on climbs to give my hand a break. I used to use bar ends on the inside of my grips, looks odd but works well and just got some new ones to fit to all my bikes for use on climbs.