engorgement issues

So basically I make enough milk to feed a small village which I'm so happy about! However, I have been feeding my baby on demand for the last week (she's one week old). She eats CONSTANTLY! She latches well too. However, my boobs are constantly hurting, hard, & tender. I sometimes manually pump only enough to get relief, but an hour or two later I'm engorged again. My question is, does the engorged feeling last forever?! I'm not going to be able to go out in public with my boobs hurting this badly. Opinions are appreciated!!