In reply to This.woz:
1) It's pretty common to have to gradually increase the number of climbing sessions you can do. I started out only able to manage one session per week, then had to work my way up to two and then three (three or four seems to be as much as most people can manage, if they're decent intensity).
Climbing puts a lot of very unusual stresses on your body, which other sports don't necessarily prepare you for. You've evidently got a good sense of when you've overdone it, so listen to your body.
2) At this stage, the best way of gaining climbing-specific strength is just climbing (sorry).
And if you're already climbing as many times a week as your body can recover from, then trying to add extra training for the same muscles is not going to help and it's just going to eat into your recovery capacity.
However, if you've been climbing for two months, then (unless you are a kinaesthetic prodigy), your technique's probably rubbish. This should be a *good* thing to hear because it means you can make huge improvements on overhangs etc. without having to get any stronger.
There's some discussion of resources for improving technique in the thread here:
https://www.ukclimbing.com/forums/bouldering/looking_for_bouldering_progres...
If you're obsessed and super-keen and desperate to do *something* to improve your climbing when you're not actually climbing, then look for stuff that won't deplete your ability to recover -- for example, maybe you could stand to work on your flexibility, or maybe some light antagonist training will help keep everything balanced.