Yes it normal. I have been leaking for the last month and a half it not longer. I'm 37w1d.
Lol yes it's normal. If you're going to be nursing that's what's gonna be feeding your baby. U can get little round breast pads though for it. U can buy them from anywhere really. They're big enough to go over your whole nipple and it'll just stop the milk from leaking on your clothes and stuff