My son was four months old when I got a plugged duct. Your description sounds exactly like what I experienced. With my case, since only one duct was clogged, only a part of my breast would act engorged, but the pain and tenderness was throughout.Â
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Things I learned to do as I battled with this on and off for a few months until it was totally gone were:
-Nurse on all fours over baby. Yeah, it feels totally awkward, but it did actually help open me up.
-Hot shower for as long as I could while massaging and massaging and massaging the area from base of breast toward nipple. I'd often bend forward so the girls would just hang there so there'd be no obstruction.
-The nurses at the bf clinic ended up giving me a sterilized needle that I had to use so many times. Often in the hot shower, after the massaging I'd actually be able to see the "coagulated" milk at the duct opening. The needle helped remove it. It didn't hurt anymore than my breast did anyway. I was always so excited to actually get something to come to the surface it didn't matter that I was taking a needle to my nipple!
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Hope this helps! If it is a clogged duct, do whatever it takes to get it cleared up asap or you'll end up with a case of masitits (i did and never had the redness).