Unless you have also got weakness in your legs, numbness and/or tingling in the legs, loss of control of bowel or bladder, or it's getting worse particularly at night, you can probably think that it's not something sinister.
If you've been particularly conscious of your posture over the last few weeks it could well be precisely because of this that your muscles are tight. You may be using muscles that are usually short and quite strong, but are now being lengthened and don't quite have enough strength, or you may be using one set of muscles but not supporting the movement with strength from the opposing set of muscles.
If your pain persists, perhaps see a good physiotherapist with experience in dance and posture, otherwise your best bet is to maintain your current regime and it will eventually settle down. ALWAYS do a cool-down stretch, NEVER stretch cold muscles (always do a bit of cardiovascular warmup first), and relax after a dance session in a warm bath or similar.
IMHO dancing per se will NOT damage your spine - you may however get stiffness and temporary discomfort from movements that you are not currently fit enough for. Most back pain does not require 'treatment' and indeed the majority of RCT's suggest that good pain relief, temporary relaxing of usual activity levels, then gradual increase in activities is all that is necessary. Osteopathy, chiropractic, physiotherapy have some evidence to support their use in the early stages of recovery (up to six weeks), but limited evidence to support their use after that - in fact, most medical research suggests that after this time the best thing to do is maintain your usual activity level, and gently increase. For excellent professional-level advice on pain, this site
The Oxford Pain Internet Site is recommended.
Stretching can also be a factor in increasing back pain - again because of the need to stretch one set of muscles while strengthening the opposing set...