Recent studies about training through back injuries. I want to see those studies, and to the OP REST. Then MORE rest that is the answer to your question. Ask your doctor "hey my back hurts after a long bike ride and trying to lift something heavy...should I do a century ride tomorrow?" and see what he or she says....
I hurt my back the same way. I ran 3 miles, then did dead lift at the gym. I herneated a disc pretty good, and was in pain for a week, and in physcially therapy for a few months to get to 100%. I'm not saying that is your issue, but I'd get checked out. In my case, this wasn't the first time I'd had issues with my back. Once in a while in a certain spot, I would tweak it once in a while. After a couple of years of trying different physical therapy treatments (no severe injury, just bugging me periodically) the PT narrowed it down to a muscle imbalance and weak core that allowed my inner abdominals, and hips to pull on my spine and bulge the disc. In any case, taking time off and working on the issue that was causing the reoccuring pain is the only thing that has worked. If you can train through a back injury, you don't have one. TRUST ME.