Can the baby's biting cause my milk duct to clog?

No. Not usually. Clogged milk ducts are usually due to anatomic changes in mom's breast, sharper angles or narrowing of a duct, which is why they tend to recur in the same spot. The baby biting will cause sore nipples or cracks, which can make the breast more susceptible to infection.
Breastfeeding. This is rather unlikely. Of course, anything is possible but still unlikely. Try a warm compress and some gentle massage to open up the milk ducts.