I had this problem constantly & found it painful, frightening & was very worried...it eventually affected my milk supply. I consulted a LC and she couldn't find any obvious reason for it (i.e. poor latching) so suggested it could be due to a high fat content in my milk. The usual recommendation for this is to reduce fat in your diet but I already have a low fat diet so she suggested I take Lecithin (1200 mg, 3 x per day) which is meant to help break the fats down. It worked. It took a couple of weeks but I haven't had blocked ducts for about two months & I was getting them every other day prior to taking Lecithin.

The white spots I removed with a sterilised needle as suggested by allycat06. This blockage at the nipple is what causes the blockage further back & for me the more I massaged, the more milk I stimulated but it couldn't get out so the pain was worse....you must clear this spot. I didn't find it painful or sqeamish at all & I have a very weak stomach for anything medical or blood or anything. I found if I cleared the spot and fed DS immediately it was the best way to clear the blockage. The only time this didn't work was when I had been blocked for days & the water from the milk had been reabsorbed by my body so the milk was very very thick. I made a warm bath, laid tummy down & expressed...lots of stringy thick milk.

I hope this helps.