Screw the icepack. Have them give you something even better:
You fill the cooler with ice and water and a pump circulates the water through the pack on your body part. They are available for shoulders because the doc that did my surgery sent one home with me. I wouldn't have been able to function without it for the first week after the cutting. The pain relief was almost instantaneous once it got turned on and I ran it until the water got warm.
But if you do get one, leave the sleeve part on your shoulder for the first day or so, rather than taking it off and on. It's easier and less painful that way.
For the first couple weeks or so of PT, take a pain pill before you go. My PT recommended this to me and it was a great suggestion. Turned the PT from a screaming painfest into an annoying achefest. Also, look into pool PT. It's way better than being in an office and being tortured.
And it pays to find a good PT. Mine was absolutely awesome and I think that's why I only had to do 4.5 months of PT after the surgery. I also invested in a pulley (they're less than $20) that I used at home a lot. Definitely do your home exercises-it makes a big difference.
I wish you speedy healing.