In reply to sip a cup: Your shoulders may be sore because you were climbing all day. Anyway, I have a few things to add:
Stretch, top tip. Sport massage will help keep your shoulders healthy and increase blood flow to the muscles. This will also help reduce chance of injury.
Climb more, naturally, that is key. However, training is useful when done properly. As we have already read, climbing uses specific groups of muscles so it is important to consider the opposing muscles too. You don't need to become a beefcake but it'll help your fitness and prevent injury if you workout a bit.
I'm sure all will agree that it's not just about strength. Mental sharpness, technique and flexibility is also important. Of course I can't comment on yours so you'll have to think about that yourself.
Stretch.
Now if you want to work on your power and shoulder strength a bit then there's one drill to try if you feel like it. Lock-off training might help. Have a look online but if you want more info let me know.
That'll do for now. Have fun out there, the most important thing.