I had something very much like this happen to me while I was finishing out the “White Man Can Jump” routine over 2 years ago. The symptoms of my injury were very similar to yours in the location and manner you describe the pain, however my sharp pains were more consistent and hurt when I bent over (as for example bending over to lift the lid on the toilet).
I went for about a year trying to rehab the back. It got tolerably better after about a month of very light squatting and deadlifting (I hurt myself squatting 355, I spent the next month not daring to squat over 185, I think I got squirrely once and did some reps at 225 - just to give you a notion of what was light and heavy for me). But even after this month backing off, the problem became recurring. I would eventually get back up in weights and then would start to feel twinges again from the injury. It was absolutely a limiting factor in my lifts - not to mention it didn’t feel none to good.
After about 6 months I went on a vacation and wound up taking the next 4 months off from lifting completely. It was sad, but it let my back get back to form - at least I thought so. Eventually I got back to what were heavy weights for me and I started feeling the twinges again.
I say all this just so you get a notion that I went through the long journey of trying to get this right on my own.
I used ice, heat, stretching, anti-inflamatories (motrin), massage, etc. it got better but it didn’t heal.
Eventually I went to a chiropractor and that got it right. He explained that the cause of the symptoms was that the lower back had been pulled out of alignment. The muscles, to compensate for the misalignment tighted and strengthened to support the ailment, creating an imbalance. The problem with this was that whenever I started strenthening those muscles again, it encouraged that imbalance and wound up encouraging the back to stay (or go further) out of alignment. He readjusted me and I started over with my squats. The end result is that this problem is gone and I’m able to move on with increasing my lifts.
I started going to the chiropractor about a year ago (I go once every two months now just for check-ups and minor adjustments) and I’ve got no problems with the back anymore. At the very least you should explore this option just to have the chiropractor see if your out of alignment. Obviously you want to find a reputable Dr. who is more concerned about fixing you than earning your business, and there are a few out there.
Some tips to help (at least what has helped me):
The injury occured because of bad form (surprise). When you squat pay particular attention to how or if you favor a side. Tons of people do this and everyone of them is encouraging a dangerous imbalance. Don’t shift your hips at the bottom, don’t turn your knees in, keep your abs tight, etc.
Stretch your hips, do it, do it a lot. One of the most under appreciated muscle clusters and one of the most influential in how we lift. They get tight and they start pulling things wonky. Before, after, that’s a difference in philosophy but doing it is a must.
Read the Out of Kilter series by Ian King on this site(this should be a given)
Make sure that your keeping a balance between your hamstring and quad dominant lifts. They may progress different but they should be progressing together, so to speak. The White Man Can Jump Series is big time squat dominant, and I was already imbalanced towards that lift over deads. This was a bad mix for me.
I used the first phase of Ian Kings Limping Series as a rehab for my back before all the chiropractor stuff. This helped for many reasons. Mainly because it’s bodyweight exercises that exposed my imbalances and forced me to correct them without putting extenuous stress on my injured back.
Good luck, let me know how things turn out for you.