T.N.
Hi K.,
Congratulations on your great gift:-) In case you didn't remember, lanolin is your best friend! You can also try letting your nipples air dry after each fed. It also sounds like your daughter may not have as great of a latch as you think she has, so I would consult your local lactation consultant just to confirm the latch.
As far as using the pump to get get things going, it is great if you are engorged. If you had a C-section your milk will be delayed typically longer than with a vaginal birth, but you should expect it within the next day or two. Also, if you supplement with formula that will slow down the process. I would feed your baby as often as she is interested. This will help with the milk supple. As far as getting your milk going, there is nothing like baby to do that. The more you demand the more you will produce, so there is truth there. For example if you are nursing AND pumping you will make more than your daughter needs, and have milk to store.
Best of luck,
T. Nelson CD (DONA)