I just saw a white bump on my left nipple and it really hurts. How do I continue breastfeeding or pumping?

Sounds like a milk blister! Before you nurse, try to hand express back behind and down toward the nipple to release any thickened milk that has backed up in the duct. Sometimes clumps or strings of hardened milk (often of a toothpaste consistency) can be expressed from this duct. Alternatively, you can consider using a nipple shield during feedings. Here's an article about milk ducts: http://kellymom.com/bf/concerns/mother/nipplebleb/