Hi, You need to get your biomechanics checked, back pain is not normally serious but will probably not be helped by running. This does not mean that you have just lost your favorite sport, just get to see an osteopath. He/ She will sort you out.
Talk to your Doc, this is of prime importance, diagnois is never made over the 'phone. But as a parallel search, talk to your local osteopath, you may have a mechanical problem which is only manifesting itself under pressure.