It's hard to tell what is causing it. it's good that you're dr. recommended the xray but if you continue having symtoms, maybe your should have an MRI to see what may be missed from the xray.
I'm not sure if cat scans are better than Mri's when it comes to back problems.
If you're dr can't help you, I would suggest you see a different doctor to get another opinion if you have these options. I don't know where you live and how easy it is for you access other doctors.

it sounds to me because of all the weight that is carried at child birth, tthe muscles in your abdomen has become weakened therefore you hold yourself different which pulls the muscles and tendons in your back, which then causes your back to hurt.
the first step may be for you to do some light excersise to help strengthen your pelvic and abdominal muscles.
you can use a heating pad too and you can take an anti inflammatory if you're able to. but first make sure it's ok with your doctor first before starting any excersise program or taking medications.

these are the few options I can help offer you as a suggestion.

child birth really effects our bodies and it takes a full year for our bodies to get back to normal again. that's what my doctor told me after having my first child back in 1982.

My heating pad has helped my back pain tremendously.

good luck and let me know how you're doing.

sincerely,
linda