It really isn't very bad at all, but I keep a close watch on all my aches and pains. I'm hoping the icing helps.
It's your choice, of course, and I wish you the best. But don't be stubborn about it, believe me. I've played through pain and exercised with torn muscles before. But I think it's not smart, especially at "our" age.
As I said before, I felt mine was "just a twinge" and it "wasn't very bad at all" when I decided to go ahead play tennis that fateful night. And even during play, I didn't really notice it too much, with just a HINT of a twinge here and there.
But the next day? Oh my! I actually could not lift my arm above my waist without tremendous sharp pain in the very same location that you're describing. Also, I could not put any pressure on my left shoulder with my right hand without feeling some very deep pain in the tricep/bone area.
As I said, it's your decision. But don't be stubborn about it, because even though it may seem like it's not "very bad", it doesn't take much to BECOME very bad, very quickly.
I don't mean to be overly-dramatic about it, but I just know what happened to me when I felt the exact same pain. It was so slight that it didn't even affect my stroke at all. But after playing that one last time, it has now been over 3 weeks that I have been recovering and although my shoulder FEELS 100%, I don't trust it yet and will continue to do some strength training and light racquet-swinging for the next week or so until I feel ready to play again.
The way I figure it, if I have to wait an additional week or two right now before I'm able to play without fear of injury, that's a VERY small price to pay to prevent MONTHS of rehab and possible loss of ability to play competitive tennis forever if that "slight twinge" develops into a full tear.
Ice is nice, but it really doesn't FIX the problem, it only helps numb the area and may speed healing slightly. Same goes for Ibuprofen - it just masks the pain, but doesn't heal the injury. Don't let it fool you into thinking that it's just a minor ache due to muscle over-use. That's precisely what I thought when my pain was just a twinge. But if it's the same pain that I had, then it's potentially more serious than that and could get significantly worse if you push yourself.
Good luck.