In reply to mopa:
There may be a genetic component (certain blood types) but susceptibility to injury is generally multifactorial so look closely at your lifestyle and training habits. The big take home from Make or Break (at least for me) is that injuries are generally the cumulative result of habitual training/recovery failures and therefore they provide valuable information on how to rejig/finetune your approach to climbing. (They are also a massive pain in the arse but you already know that).
Key things to look at are:
How much sleep do you get?
How good is your diet?
Are you stressed at work or working long hours?
Is your posture good? (Really important given you have a sedentary job)
Do you have a balanced training schedule that includes cardio (active recovery), flexibility work and antagonist training? (the second two are crucial)
Do you have any pre-existing injuries/joint instabilities/muscular imbalances?
How are your training sessions structured? Are you limit bouldering 3 x per week? If so it's not a surprise the wheels are falling off. Personally, when returning from a lay-off I can boulder hard once every ten days, throwing in occasional high volume sessions strictly at lower grades. This definitely puts me in the bottom quartile of training frequency and it's frustrating, but when I get excited and ramp things up too fast I pick up injuries.
How varied is your climbing diet? Is all the bouldering at one centre? Do you spend a whole session working one project? Restricting yourself to two attempts per problem per session is a good ground rule for avoiding tweaks and forcing you to read the sequence properly before starting. If you can, try to do some lead climbing, it's less brutal than bouldering.
In the short term, I'd suggest you rest until your shoulders have calmed down a bit (don't charge into rehab if they're inflamed, you'll piss them off more), just do some eccentrics for your elbows and some wall slides (back off if your shoulders flare up) on a daily basis. Then add in face-pulls, strict form tricep pressups and reverse wrist curls whilst easing back into gentle climbing. Also yoga. Lots of yoga.
Good luck!