Congratulations for the baby.
It is possible that while nursing her baby or while lying, your wife is not maintaining correct posture. This can result in muscle spasm of the back and can cause pain.
can be due to acidity and gas and will be relieved by dietary precautions.
If the pain is persisting you can get her examined by a medical professional. Donot self- medicate as some medicines are to be avoided in mothers who are feeding their babies.
If you have any furthur query, I will be happy to help.