It feels better now. But still not back to normal. Funnily enough the shoulder feels better after a squats session. Probably the positioning of the shoulders to the bar has relieved the pain somewhat.
Doing pushups doesn't inflict pain on the shoulder though. So probably I'm gonna have to just settle for pushups and bodyweight rows and perhaps dumbbell floor presses for my upper body training sessions.
Hopefully my shoulder will recover very soon. I miss overhead presses already.