A slip on recoil pad is the quickest, easiest fix, but it will add some length to the stock and that can alter the way the gun fits you. Worth a try, though. Otherwise, try lighter loads if they will still do the job for you.
But then....you need to learn how properly to mount a shotgun and shoot it with an aggresive, lean into it from the hips, and let your full body weight help you manage the recoil.
Common mistake made by folks using a shotty for the first time and it is TOTALLY understandable, is to try to "shield" yourself from the recoil by actually NOT getting your cheek weld on it, nice and tight. Don't bring your cheek down to the stock, get it up to your cheek, and again, be sure to get your full weight behind it from your hips.
If you are doing it right, you actually will have more of a sore cheek than a sore shoulder.
I only weigh 125, and have had both my shoulders separated due to foolish skiing accidents, so not only am I lightweight but have "soft" shoulders to boot. I wanted to try skeet/trap shooting and picked up a 20 ga 870 and was rather surprised at the recoil, not much less than a 12. The new recoil pads are effective, I bought mine from Remington and was stunned at its performance. Perceived recoil was about 50 percent less. Bought me a new O/U 12 ga and will get an aftermarket recoil pad for it, probably the Limb-saver.
There are some auto shot-guns such as the Berreta A400 with integrated stock buffers and other goodies that reduce recoil but they are kinda pricey. A good recoil pad seems to be the least expensive, easiest solution.