A whole host of problems could be causing the
back pain, but running could certainly be one of them.
Physiotherapy is essential, and you will need to stretch in the long term. However, in the short term, you MUST NOT OVER STRETCH THE PAINED AREAS. Indeed, a back brace/strap is essential to support you through this acute phase rather than pushing through with excessive therapy.
Heat and cool therapy will also be excellent, and I would recommend
NSAID medication such as
ibuprofen.
If you are carring any injuries in your knees or ankles, or if you have a problem with your instep or gait would also be exacerbated by jogging, and could "jarr" your back. I suffer from this terribly with cycling; which forces me into uncomfortable positions for long periods of time, and also when jogging on my arthritic left knee.
Typically, back pain is a
muscular pain, and will tend to "move around" as different lower back muscles take up the strain at differing times.
A back brace may help with this and enable you to continue to jog. alternatively you could look into the probloems I suggested above.