Look into getting one of them "slip on" stock pads. They will really help in knocking down the "hurt".
My 870 would knock the snoot out of my shoulder when testing 3" buckshot loads, but I finally got smart and used a slip on pad.
Orvis makes a removable shotgun pad that works very well. It comes in sizes from XS (4 13/16"L x 1 7/16"W) to XL (5⅝"L x 1⅞"W) It does add 1/2" to the length of pull on your shotgun. You'll want to measure the permanent recoil pad on your shotgun if you have one in place or just measure from the top to the bottom of the butt if there is no permanent pad, and then order by size.
Here's the link to the
Orvis Leather Recoil Sleeve And Pad
Here's a picture of that removable recoil pad:
I used to do Custom Shotgun Fittings for the Orvis San Francisco Store back in the 90's and more important than a second pad, is proper shotgun mounting technique. I often had to instruct folks on how to mount the shotgun properly and consistently because if you don't mount it correctly, the instinctive shooting method that Orvis teaches won't work. If you could mount the shotgun repeatedly (10 out of 10) then I could use our "Try-gun), which was infinitely adjustable, to make it shoot where you are looking when you mount it. After adjusting the gun, then I could measure it and send the specs to our stockmakers to build it as well as checker it and engrave the side-plates. Our over/under customs took 2 to 3-months to complete whereas the side by side shotguns usually took 6 to 9-months.
The whole idea on fitting a shot gun is putting your eye in exactly the same place every time you mount the gun without leaning your head over or trying to adjust your sight picture. When the gun has been fit for you, that shotgun will shoot where you are looking. But that totally depends on proper gun mounting. Using that method you focus on the target and when your shotgun is mounted, you fire because you are already on your target.
There is a pocket on your shoulder between your shoulder joint and your collar bone. (clavicle). It's a natural depression and that is where the butt of your shotgun needs to be mounted. The entire surface of the pad should be in contact of that pocket. If you are using a 12ga. and you mount it a little ways to either side, too high or too low and you will bruise your shoulder. DO NOT mount the toe of the butt (bottom point of the shotgun butt) in there without the rest of it touching. You will see military folks put that toe of their rifle butt there so the rifle sight is closer to their eye level. They can get away with doing that because they are firing a .22-caliber round (.223/5.56mm), which has very little recoil. Do that once with your shotgun and your shooting will be done for at least the day if not a week. That is NOT a proper mount for shooting a shotgun.