Hi C.,
Just hang in there and give it 2 weeks. Things will get much much better soon. Here are things that will help with engorgement:
1. Cabbage leaves. Peel a nice green one off and bruise it with a rolling pin. Put it over your breast for about 20 minutes.
2. Hot shower - massage your breasts in the hot shower - you can actually push some of the milk out, and this will help
3. The ice, as another poster mentioned.
Also, if you haven't started now, get some lanolin or olive oil to put on your nipples after you feed your girl. This will help keep them from getting chapped and dry.
After 2-3 weeks, I PROMISE, breastfeeding will have turned from a chore into a very nice thing. Plus, it beats the heck out of getting up and messing with bottles in the middle of the night.
Hang in there - and good luck!
Edited 2/19 to add this comment:
I agree with other posters about getting a good nursing bra. I love the Bravado bras and wore them 24/7 (yes, sleeping too) for the first several MONTHS that I was nursing my baby. You can order them online. www.breakoutbras.com has the best prices I've found (and free shipping). Also, BellyDance Maternity in Bucktown sells them if you want to try them on. They're expensive but worth every penny.