Thanks, I'd like to think I know my shit.
Look, there are many schools of thinking about how to address this. One way is use meds to ease the pain and go about your daily activities. I'm against that. Anti inflammatories essentially kill the pain, but they also kill the cells that come into the muscle and eat up all the cellular debris that needs to be cleared out. Whenever you use meds in these circumstances you delay the healing of the tissue - but that's up to you.
The ideal way to deal with this,
in my own opinion, is to let the inflammation resolve on its own. One reason for that is - the pain will give you a good estimate as for what type of movements you want to avoid, those that put stress on the inflamed tendon. Next, you want to keep the joint mobility going, despite the pain. What could be done is simple physio exercises such as abduction-adduction, and rotation along the shoulder joint intermittently throughout the day. Stop at the range of motion where the pain is very intense. It's going to be a bit harder in the morning, but that's when it's going to count more.
Avoid abduction on the horizontal plane that places pressure on the pecs. (Any movement that is like the "pec fly" machine)
Do not lift, do not work the pec, but you can do cardio as long as the shoulder joint is very minimally active on it (such as ellipticals). Cardio may actually increase rate of recovery.
Next - diet. I know it sounds stupid, but people downplay the importance of proper nutrition on tissue regeneration. I don't mean calorie deficit, I actually mean good sources of complex carbs and protein. Recently Dylan posted a good video on it, Here's the link:
https://www.youtube.com/watch?v=WzHZkDw84h8
Take it super easy on the sugar and all high GI foods - hey tend to increase the duration of inflammatory processes.