That's awful, I've had those bad sore throats, too. Fortunately not while breast feeding as I recall though.
What about Cepacol cough drops? They have benzocaine which numbs the throat. What I've done is suck on it till its numb, then wrap the drop up in the wrapper till I need it again. It lasts longer that way and you don't need the whole thing.
I also drink a lot of ice water just because it feels good on my throat. Drink before the drop though or the effect might not last long.