The problems with hand and overall pain in the upper torso and shoulders result from poor bike fit and not changing ones position frequently enough while riding. In addition to changing your position on the bike you can have the fit checked and see if the stem needs to be raised or changed out altogether to provide the proper reach for your body. I would trust at most one person in ten in a bike shop to be able to do this.
For road bikes I change my hand position continually and have my hands on the bar and then on the brake hoods and on the drops. I primarily use the drop position when going up hills and seldom on the flats. My neck suffers if I spend too much time down on the drops.
Going gloveless will only make the problem worse. On my older bikes I always changed out the handlebars for larger diameter ones like those from Cinelli and then I would wrap the bars with thin foam sheet that allowed me to control the thickness of the addition to the bar at different locations. Last step was to add handlebar tape and on the drop sections there was only the tape. This maximized the contact area for my palms on the handlebars and reduced having a pinched nerve, which can cause permanent damage.