I usually use thin shooting gloves on range (full or 3/4 finger), but then I'm usually shooting several guns and many rounds. In real life use, doubt I would notice the pinch or bite, but not going to let my fun on range be uncomfortable, so recommend gloves. YMMV
This is what's happening: I am guessing here you have large hands or chubby hands (I have the latter). As the pistol fires, the pistol wants to pivot up, driving the top of the tang into the web of your hand, enough to roll just a little skin onto where the hammer meets the tang. Just in time for the hammer to catch it and give you a love bite. Try gripping slightly lower, and check between shots to see if the pistol grip slips down in your hand. So far I have had 2 pistols that did that to me.... now they belong to the wife, lol. Her hands are much skinnier than mine. I then got a pistol with a nice beavertail (para and taurus pt1911), havent had a problem since.
Or you can just keep going until you build up a callous. Cheer up, its better than slide-bite. One of mt relatives shot a little beretta 25 auto, put both thumbs behind the slide (one on top of the other) and sliced into the thumb knuckle enough to leave blood all over the pistol and needed immediate bandaging.
Lightweight flexible gloves - I use mechanix brand. I use gloves when I am testing a newly repaired or serviced firearm,and occasionally when shooting big caliber revolvers/pistols. Cheap fix , and will protect your hands should something bad happen , or your grip slips a little and the back of the slide finds your hand.
I suffered hammer bite when initially shooting my RIA 1911. It was of the original hammer and grip safety design. I ordered and changed out the original hammer and grip safety with a Wilson Combat hammer (with new strut) and a Wilson Large Beavertail grip safety. No smithing required as these were all drop in parts. Took care of the hammer bite too!