(Disclaimer: I'm not an exercise professional or coach, however, the below advice is a distillation of some good advice I have actually received from some professionals)
I went through the same pain recently when I upped the training intensity (too much bouldering combined with fingerboard). Try the following:
1) Take some Neurofen for a couple of days - this will loosen things up a bit,reduce any inflammation you may have and better enable the following to help repair the body
2) Do push ups before and after every training session (this works miracles, trust me)
3) Warm up thouroughly before every workout and STRETCH!
4) Lower the intensity: Keep training, just stay off the crimpy stuff and use it as an opportunity to work technique
5) Go into every workout with a plan - eg warm up drills, some endurance work and a couple intense goes at a project - don't just go in and flail at every hard route in the gym. This should fit into an overall weekly, monthly and possible micro-cycle plan (eg Horsts 4-3-2-1 training cycle)
6) Read Julian Saunders' article on how to avoid this (has some good stretches and other exercises)
If nothing else, start incorporating some push ups into your daily routine.