I had same when I gave birth to my baby. I was really disturbed. Please note that Inverted nipples don't say anything about your health. You can even breastfeed normally: While babies can have a bit more trouble latching onto an inverted nipple than a protruding one, a little patience while you position yourself and the baby can make it easier for the baby to feed. You can also ask your doctor about special breastfeeding devices, such as breast shells, that help pull out and position an inverted nipple in a way that makes it less difficult for the baby to nurse.

Truly inverted nipples are caused by adhesions beneath the nipples that bind the skin to the underlying tissues. They're actually quite common; an estimated 10 to 20 percent of women have flat or inverted nipples. For some women, nipple stimulation or cold temperatures can draw the nipples out temporarily. How do I breastfeed with flat or inverted nipples?
Make sure you get a deep latch. If your baby can open wide and close his mouth further back on the breast, he'll be able to latch deeply onto the nipple, areola, and the breast tissue underneath. Clamping down just on the nipple is not only inefficient for drawing out milk but can also cause nipple damage and pain.

To help your baby get a good latch, place your thumb on the top of your breast, and position the other four fingers of that hand underneath it. Pull back slightly on the breast tissue (toward your chest wall) to bring out your nipple. Brush your baby's lips or cheek with your nipple to trigger his natural feeding instincts. Once he opens his mouth very wide, hug him into the breast, aiming your nipple toward the roof of his mouth. When he latches on, his lips should be splayed out.