If there were a connection with the BC it would pretty much have to be during above-water maneuvering, as almost everyone I know with any sort of back or neck problems feels great underwater in weightlessness.
Does the BC (with tank) cause a lot of pain when worn above water? If so, it may be a local pressure point that may need a pad added or a change of BC.
If it doesn't make the pain worse above water, it's probably not the BC.
The weight of gear we commonly carry and handle in surf or pitching boat decks while walking on rocks or wet surfaces is ideal for a minor muscle strain to occur, and gradually develop into a major pain.
If diving were regulated by OSHA (the Occupational safety and health administration for the international readers),
the loads we carry and the surfaces we traverse would give an inspector fits!
I certainly don't want them poking into my personal activities or regulating our favorite sport, but we need to remember the risk to us "weekend warriors" that have physically soft jobs all week and do more challenging things on the weekend. (myself most definitely included.)
I'd bet that some little jerk or misstep or slip caused a strain and it has escalated from there.
If you have pain or numbness or weakness in an extremity, that might suggest a pinched nerve somewhere and needs a medical exam and evaluation.
If you have an isolated sore spot with no sign of anything else involved, I'd probably try resting it, pain relief, and local Ice alternating with heat like you would for any other minor strain or sprain.
If it's not getting better in a week of home therapy, get it checked out.
Most minor pains are just that, minor pains. Get them checked if they become major or have other symptoms or keep going longer than a normal minor strain or injury would.
Dive safe and painless;
John Reinertson