I've had surgery on both shoulders (at different times). The first one (my right shoulder) was the worst. The rotator cuff was torn almost completely off where it attaches to the large bone in the upper arm. They literally had to drill holes in the bones of the shoulder and arm, then use something like rawhide laces to tie it all back together. It took a year before I was back to normal. But yours can't be that bad if they're just doing it arthroscopically. Mine was major surgery.
My left shoulder rotator cuff needed surgery several years after the right. That also required major surgery, although it was nowhere near as difficult as the right shoulder.
You said you're right handed, but didn't say which shoulder they're working on. If it's your right shoulder, here's some advice. Start practicing doing things with your non-dominant hand immediately. Little things that you don't think of, like brushing your teeth. I wound up brushing my face a couple times when the brush slipped out of my mouth.

You might THINK you're fairly ambidextrous, but you'll be surprised at how awkward certain seemingly simple things can be when you're forced to use your non-dominant hand.
The physical therapy can be a pain, but it's critical. Those folks know what they're doing, and can get you back to normal a lot quicker than you could on your own.