Does a white spot on my nipple while nursing mean I have a clogged milk duct?

Probably yes. A white spot on the nipple of a breastfeeding mom probably is a clogged milk duct. There are other skin glands, such as oil glands, that also can clog and be seen as a white dot. A doctor can gently remove the whitish material at the skin surface, and then the mom can see if the spot returns over a couple of days.
Could be. You can try massage and see if you can unclog it. A white spot on the skin may signify vasospasm- try warming your breast and see if it helps.