In reply to richrox:
Just to chip in I have have a depressingly large amount of experience recently with this kind of injury.
General rule of thumb is the RICE protocol. If this doesn't help then take a full week of rest. If it doesn't improve with full rest then it won't get better by itself. Your trekking trip is clearly full rest, at least for those parts of the body anyway, so you need to do something.
I have had good experience with physioterrorists dealing with muscular imbalances, locked muscles and finally a partial tear of the supraspinatis, part of the rotator cuff.
The rotator cuff was diagnosed as a shoulder impingement from my GP, but I asked for the ultrasound which showed the partial depth tear. This is at the mid to high end of the scale of injuries, and took 7 weeks rest followed by 4 physio sessions spread over 5 weeks to get back into training. Training started earlier than this but I wasn't allowed to do overhead movements until then.
The suggestion of going to the doctor is a good one but NHS physios are not hands on, they'll just give you a series of exercises. It's the massage and manipulation that does the work. The other thing is that some areas have excellent physio services and others will take several months for a referral. I always go private.
Physio was £45 first diagnosis sessions then £35 per half hour.
From the exercises suggested, I would say don't do back lever with an injured shoulder - I still can't without pain and I managed to get a full back lever a couple of years ago, and as suggested treat deep dips with caution, since they stretch out the front of the shoulder. Front lever and row work will have a good carryover to climbing...but maybe you need some balance with pushing exercises....?
To see if it's rotator cuff raise your straight arm out to the side, all the way to vertical. If it is pain will be in the shoulder as you come beyond the horizontal.
Good luck with your treatment.