Definitely don't sleep with weight on the shoulder until the pain goes away. That helped me and was a good pointer from my physical therapist. One option for side sleepers is to get a special pillow or position several pillows so that your weight is not on the shoulder. Check out the web site
http://shoulderpainatnight.com/ for an example.
Often shoulder issues are tendons that are inflamed from catching on something, most often the AC joint (impingement). So you want to increase the space in the AC joint by keeping your shoulders back. Ways to do that are
Not sitting at your computer too long with your shoulders pulled forward. I like a break with my hands behind my head POW style.
Being conscious during the day of keeping your shoulders back.
Strengthening back muscles to counteract the forward pull of the big chest muscles
Strengthening the rotator cuff muscles (throwers 10)
Chest and shoulder stretches.
Hanging by your hands. Don't need to hang your whole weight.
One guy wrote an entire book stating hanging helps with impingement. I just saved you the cost of the book
Don't know if it helps but I try to use a neutral grip when exercising (lat pull downs, hanging by hands, using rowing machine, bench pressing with cable machine). That seems to be less stressful to my shoulder.
And you want to determine if your tennis serve is causing problems.