I had serious issues with sore hands & inflamed tendon across the palm of my hand a few years ago, was using ODI ruffans grips, (which in hindsight are some of the hardest grips out there)
I played around with a few different grips to sort it out, found that grips with the the small rubber ribs across them worked best for comfort & vibration,
found these BMX ones from ODI that are lock-on as well,
they are mint !!! been using these for 4 years now with no hand issues at all any more, even ride all day in the park when its hot with no gloves, no worries.
my advice would be to buy a similar cheap non lock-on pair to try for a start, if they work then get the ODI's
As another idea, try shifting your brake lever position a little too, experiment run by run, my mate had similar issues to me & ended you changing the position of his brake levers, which in turn changed the position of his hands on the bars, symptoms & pain went away, took him a while but worth it in the long run