In reply to jules699:
Yeah just largely re-iterating what's already been said.
Pay attention to your warm up, warm ups are really personal and what works for your mate might not work for you. Your mate might get away with 5 minutes on easy problems, personally I need an hour plus if I'm going to be pulling hard on small things. The only times I've acutely damaged fingers or finger flexors has been when I've rushed a warm up for some reason.
Sounds like what you are experiencing though is just overuse. It's a tricky one to balace, personally I find managing finger injuries is a big part of getting training right.
The key is knowing when to back off and having strategies you can use to mitigate how much worse you're making things when you train. Tape and being meticulous about your warm up can help prevent things getting worse. Icing after every session, ibuprofen, active rest and sports massage can variously reduce inflammation and get blood flow going, which improves healing.
Sometimes though what you just need is some days off, I personally don't find taking a long stretch (eg. weeks or months) off climbing useful, as within a session or two fingers seem to be back where they were before. I think active rest eg. easy traversing, finger putty, stress balls, anything to keep fingers moving and blood flow going, more effective than stopping entirely.
Climbing on plastic is often more stressful than climbing on real rock, bizarrely I sometimes come back from a week away with fingers feeling great, only to find them throbbing after the first session back at the wall. Try mixing it up at the wall: different angles, hold types, grip types, styles of climbing, bouldering, routes, different wall, etc. to try to spread the load a bit.