Some different advice-- I'm a pumping during work mom, so I've dealt with MANY bad plugged ducts.
First, be rough on your nipple with a washcloth. ALMOST EVERY plug I've had has a white spot hidden just slightly below the nipple surface that needs to come out. In the bathtub (after soaking in hot epsom salt water for awhile boobs down), I scrub the nipple, then disinfect my fingernails or a tweezer/pin and pinch my nipple. whereever there is a white spot but no milk, I scrape a little.
NOTE: This is terribly unconventional advice, and many people will say it will cause an infection but it is the ONLY thing that works for me.
Then start to press on the hard spots and see if you get a stream of milk yet. If not, scrub/scrap a little more (not to the point of pain). If I do this for awhile and it doesn't work, I either suck the nipple HARD myself or tell my partner to suck HARD until he tastes milk.
Then I put on the pump at the highest suction, lean over, and massage the heck out of my breasts until they are drained.
For me, I have to deal with the issue from the nipple AND the breast tissue, not just the breast tissue.
I use a lot of bactroban ointment or All Purpose Nipple Ointment after so that no bacteria gets in.