Hey mate,

Sounds like we share alot of the same interests! I'm a climber and a pianist also. Though I found the best thing was for me to climb before my piano exams (guess it's finger memory and I play better once they relax post workout).
I think you meant Abduction not adduction?
The mechanism of injury doesn't make much sense because you just woke up with it... but yea your symptoms do sounds like a bursitis or supraspinatus tendonitis, though there are some things in there that would make me consider other pathologies and I'd need to examine it to differentiate.

With the inflammation of bursa or Wikipedia reference-linkrotator cuff you'll find that the scapula-humeral rhythm is affected... this means you don't co-ordinate the movement correctly and everytime you feel that pain it's because you are pinching the tendon or bursa against the acromion - which will only inflamme it further. Hense you need to avoid aggrivating factors, utilise ice and NSAID's to reduce the swelling and then undertake a gentle and graded strengthening program to strengthen the Rotator cuff and correct any co-ordination issues.

What this means is that you really aught to visit a physio... I say this because although you may be right... shoulders are tricky - and in black and white they can give symptoms for one condition when really it's actually something else. You need a physical examination of the shoulder to get a correct diagnosis and appropriate exercises.

Have a good one.
Pudding