Yeah, get a bike fit. You are putting to much pressure on your hands. You could be compressing the nerve where it runs through your palms. Make sure your elbows are slightly bent while riding. Helps to absorb the shock of bumps in the road. Get some gloves, but more padding isnt always better, it can squish into places we dont want it. Also change hand positions often it helps.
EDIT: I see you had a fitting done, talk this over with the fitter. Any reputable fitter will help you sort this out.