In reply to OneLifeOneHeart: Yes clicking shouldn't be too much of an issue?? My knees (used to) click every time I bent them and I was 19 at the time. For some reason they don't anymore even though I walk a lot more than I used to....
Most of the time climbers pick up tweaks (I've had sore elbow tendons, a deep pain in my shoulder but these have all disappeared short lay-offs) but it's only by (ab)use once the tweak is picked up that they'll turn into injuries (my wrist is an ongoing pain in the -----). Often a few days off (and possible modification of normal routine) will sort them out and stop it occurring again. For the really unlucky it will be a pulley snapping in a finger or a shotgun in the forearm because they pulled too much on a mono or something. But that's real unlucky, and then you're talking a couple months off.
It's right though to get concerned about the shoulder. They've great flexibility, but it also makes them unstable. Treat them well, I dread to think about the day I injure mine. I've heard of people never recovering from rotator cuff injures - bit scary.
But ultimately I think everyone will end up picking up tweaks sooner or later. Maybe the real skill is knowing when to worry and when to rest and let it recover.
To answer your question, physio seems the obvious way to go. Maybe get the shoulder checked - although I know people (inc. myself) with clicking joints that aren't an issue, I'm sure as hell not a doctor either.