Hi Blur,
Is the clicking actually causing you any pain? Normally a clicking without pain is a sign opf a tightness in a muscle, and the click is when that muscle passess over a bony prominance. What I would advice is stretches of the shoulder to loosen it off. Due to the rock climbing I would suggest that pec stretches would be the place to start. To do this, stand in a doorway and put your forearms on the door frame, then lean through the door and you should feel a pec stretch. If you do this how does it feel? Tight, pain?