The nurse at MCH taught me to use a needle and sterilise the needle with alcohol and then pick the white spot (like what you would do if your finger got wooden pick). The white spot is the milk that got dried up and it stuck the milk duct. The baby's sucking motion can suck it out but if the spot is too attached, it will be quite hard for baby to suck it.
I tried to pick with needle last time, it works fine. The nurse also said even if there is blood from picking, it's still fine to feed the baby.
I know the bad feeling and I hope this info helps.
I got the same problem before. My OB doctor used a needle to remove it for me. If the blockage is not too serious, it can be removed when baby is sucking. For my case, the blockage is very deep, so must use needle.