I am sorry to hear you are suffering terribly with back pain. If the spinal/epidural is performed in the standard manner, then you should have nothing more than soreness temporarily. Women sometimes develop back strain during pregnancy or labor that can get aggravated.
Congratulations for your baby.
If you are having a pain which really "shoots" or radiates downward into your buttock or down your leg, you may have a spinal disc which has irritated a nerve root. This may require treatment to soothe the irritation. Treatment might include massage, chiropractic care, and/or medications. Most back aches go away within six months with or without treatment. Childbearing, delivery, caring for a growing infant, bending and twisting, prolonged sitting, and aging all are causes of disc "bulging" and nerve root irritation.
Many times pregnancy itself whether from the weight of the baby, or the hormones that relax for back and pelvic muscles, or poor posture because of the full uterus is the cause of back pain after delivery. Pregnancy hormones sometimes mask this pain while pregnant and as their levels go down after delivery the pain becomes more apparent. Especially for the caring mother that is now carrying the baby.
If the epidural injection was complicated, like many attempts were done, and some of them landed where they’re not supposed to be, it may cause some postprocedural pain, although unlikely to become chronic.