Might be worth asking around for an Osteopath or Chiropracter who rides and can give advice. I have poor core stability (very common in cyclists) after effectively giving up something that gave me a decent level of core (Sailing). I also have weak hips, and this leads to some problems with my SI joint. Generally, stretching properly *Really* helps, before and after riding, but I do occasionally need treatment. I can't stress the importance of stretching enough, though - if you don't do it, learn some basic stretches at the gym / Chiro / Physio / Osteo and do them religiously.
It's quite difficult for bike shops to give advice on fit, as it can open them up to liability (Hurrah for no win-no fee lawyers!), but a good bike shop might give you a few pointers.
It's also worth trying a couple of the fitting services that some places offer; they'll give you an idea of whether something is wrong with the bike set up, as well as with your bike.
As various have said, try adjusting stuff - but adjust one thing at a time:
1) Try flat pedals - using badly-set-up SPD cleats can cause problems further up in your back. Riding flats for a bit might isolate a problem you didn't know you had.
2) Adjust the saddle fore and aft so the middle of your knee is over the pedal axle with the pedals at 9 and 3 O'Clock.
3) Adjust saddle height so your leg is straight (not extended / hip tilted) when your heel is on the pedal axle with the pedals at 12 and 6 - obv. the one at 6 O'Clock! Then revisit fore and aft measurement - it will have changed a tiny amount, or a lot if you have a bike with a weird seat tube angle, like a Maverick or Commencal.
4) Now try tweaking the front of the bike; try a couple of stem lengths and heights if you can - a good bike shop will let you give 'em a go if you go at a quiet time, know them well, ask nicely and bring donut or beer shaped bribes. Along with stem length, try bar height, width and sweep.
There's no easy, cheap fix for this if the bike's wrong in the first place - which is another thing. If the bike you ride is too big or small, that can also have an effect.
Oh, and finally, and this is for any ambulance chasers listening, this is partial advice on an internet forum. Of course it's boll0cks.