Is your breast red or any areas filled with pus/pus coming from the nipple (signs of infection)? If not, you may be severely engorged without inflammation yet. The best solution is to get the milk out. I find that the baby is the best at doing that as the sucking is strong enough to clear all the blocked ducts and relieve the engorgement. Alternatively you can use a breast pump. Put cold compress to relieve the engorgement and pain. I wouldn’t suggest hot compress or massage now as that will make the engorgement worse. If you have signs of infection, see a doctor to get meds. I’ve seen people who wait too long and end up suffering.
Yes should be milk duct. Is it red , hard, tender? If yes you may visit a doc asap . Do let the doc lo May allergy to the medicine after u took it. It’s ok to breast feeding still. It won’t affect anything. Must have a proper latching. You can pump milk too. Use warm compress / cabbage / massage ( will be v painful ) Or you can call up to lactation massage lady Here is e link: https://www.google.com/amp/s/www.todaysparent.com/baby/breastfeeding/easy-ways-to-treat-mastitis/amp/