Could be Mastitis. It's inflammation and pain in the deep breast tissue, usually caused by bacteria. It can appear suddenly, often in the early weeks of breastfeeding. Mastitis can cause itching and pain both on the skin and deep in the breast tissue. Here are some references. Best to see your doc if it persist.
Hey mama, I experienced this too while breastfeeding and found that moisturising did wonders! I also aired the breasts as often as I could - in this humid weather a lot of moisture gets trapped which contributed to the itch I was having. Wearing a loose fitting bra helped me too :)