Hi B.,
I am a lactation counselor and my best advice is to go into a lactation consultant's office now and have them help you through a complete feeding. If you are in the twin cities you could call Abbott-Norhtwestern's Infant Feeding Center at ###-###-####. Otherwise, the hospital you delivered at, or that discharged her should be able to refer you to a lactation consultant. La Leche League is another source of support, though volunteer based and I believe that their website is www.lalecheleague.org.
I would also recommend starting feedings when she is sleepy and not super hungry, she may be more agreeable to trying the breast then. Spending lots of time with your bare skin against her bare skin (wear her inside your shirt, with her naked except for diaper) can help, too.
An option that has helped some people in similar situations is to use a nipple shield. These devices do have drawbacks (potential to reduce milk supply, damage nipple if used incorrectly) and should be used under the guidance of a lactation consultant but they are available online and at some stores like babies r us.
I know this is a very tough time. I am sure it is exhausting to be up so often in the night, and it must be very difficult to struggle at each feeding with your baby. If you can hang in there, and get help, it is very likely that your breastfeeding problems can be solved and that you will be able to feed your baby with less work than it takes now. No matter how things turn out though, feeding-wise, she is a lucky baby to have such a loving and caring mother. Best wishes to you.