I had a SLAP tear (superior labrum, anterior-to-posterior) about 8 years ago. Initial diagnosis was some kind of rotator cuff issue, and they sent me to PT for 3 months, but it didn't get any better. I made them gimme an MRI at that point, and from that, they were able to tell quite easily that it was the SLAP tear, and scheduled me for surgery.
Trying to self-diagnose and then go to the doctor and tell them what is wrong is probably not going to be very helpful. Many of those symptoms are probably not related and would thus be red herrings as far as diagnosis goes (it sounds to me like you have several issues going on--pain at your elbow is probably just some tendonitis, pain in your forearm and wrist might be carpal tunnel-y stuff or something else, musclular crap between spine and scapula=who knows?, but the pain at the top of the bicep/front of shoulder + the clicking sounds like your money symptoms for some kind of shoulder injury). The things you think might be symptoms of something might be nothing, or might be indicative of some condition you've never heard of, and the doctor is going to ask you whatever questions they're going to ask you regardless of what your hypothesis is, because they can't make a diagnosis based on your diagnosis, they have to go through their process to figure it out. Which doesn't mean they will necessarily get it right (as happened to me), or give you a treatment plan you like, so you may want to go with second and third opinions, and be pushy about getting an MRI, and maybe be prepared to pay a lot, since insurance sometimes dictates your course of treatment. I.e. insurance doesn't want to shell out a couple $K for an MRI without seeing if PT and NSAIDS will take care of it.
The shoulder is a real clusterfuck of muscles and ligaments and tight space all trying to swing your arm around like a fucking helicopter and pick up a million pounds off the floor (you are DL-ing 1M lbs, right?), and it might also be stemming from your tight upper back--as you said, working some of that out alleviates the symptoms somewhat. Maybe you should dig up some stretches for your shoulder, wrist, and forearm (there are great wrist and forearm stretches on WebMD under the carpal tunnel and tennis/golfer's elbow sections; they probably have shoulder stretches too), and do them religiously a couple times a day for a week or two and see if you have any improvement. I thought I was going to need surgery for a torn meniscus a while back, but the knee doc said that, yeah, I probably had a small tear, but it was in any case not worth operating on, so why don't I try some hamstring stretches and NSAIDS and just ease off it for a couple weeks and see how it goes. Stretching turned out to be totally money, and any time it acts up, I lay on the stretching and it chills out.
Good luck with your shoulder, in any case. After my ordeal, shoulder issues scare hell out of me.