Thanks for asking your question in Just Answer.
You mentioned about pain on both sides of your lower back, which suggests musculoskeletal in nature ( 'muscle spasm').
Muscle pain can get worse with breathing.
Other possibility is pain from your kidneys, but this pain is usually severe, dull & moves to your groin.
You should also have urinary symptoms like discomfort on urination, blood in urine etc.
Kidney stones while passing through ureters ( tubes connecting kidneys to the bladder) may give rise to this kind of pain.
But, reading your description, muscle sprain or spasm is likely explanation.
You can try analgesics like motrin, aleve etc. along with meuscle relaxants like flexeril for relief of pain.
Try hot compress which may also help.
Chiropractor therapy may also be very helpful.
If persistent or worsening, then you should see your doctor.