I'm down with PBob on this one, The fact your feeling twitchy doing things like "moving a bin, leaning over etc" is indicative of low back because you are flexing the lower spine. Not to go into much detail but if your getting problems when you flex the lower spine the logical thing is to do back extensions as per a Mckenzie based approach (The McKenzie Institute - Welcome to the McKenzie Institute International). Again keeping it basic - an exercise that you can try is a backward bend much like the Cobra position you see in Yoga, the point is to be repetitive with it. Do it like a pressup but keep your hips on the ground. Do about 10 5-6 times a day.
This is a simple exercise you can try that I'm confident you will be able to manage with little risk (based on the small amount of information you'v given about some of your workout activities).
What I'v described is both treatment and diagnostic - if it doesn't make a difference then it's likely that the problem is not coming from the disc's of the back and I would suggest you visit someone to get a more thorough assessment. It could be a neural tension issue which can be assessed and then the correct exercises given for example.

All the Best,
Pudding