Usually nipple pain is caused by improper latch on. Then it gets worse because her pain can cause her to dread feedings, and in the meantime baby is not getting as much to eat as she could (because bad latching means less milk) and so is hungrier, thus working harder to get mre while not latched on properly which hurts even more. When the cycle repeats, often the result is that nursing is ended.
Which is by no means an irreperable tragedy. But it is a real shame to stop nursing for something that is usually easily remedied – and an even bigger shame to have to have that much pain if you don’t have to.
Normal discomfort starts about the second day and gets better around the fifth day, and has to do with how much milk is being produced. But while everybody’s pain threshold is different, it should not hurt like hell. If you are counting the hours to a doctor’s appointment I figure your wife is dealing with more than the usual discomfort.
Since so many people did not grow up around nursing babies and don’t have practical family support because of that, I will say something very simple: Visualize a circle around your wife’s nipple, about an inch in radius, not diameter, from the middle of her nipple. At least that much of her breast should be in that baby’s mouth when she is nursing. A lot, that is. More than you think ought to be possible with such a small mouth. If it feels to your wife like a pinch or sharp bite when baby nurses, baby is not latched on properly. Breastfeeding.com has got video online so you can see what it is supposed to look like.
Nursing is a dance with two partners, and bad latch can be either a problem from mom’s side (engorgement or flat/inverted nipples or what have you) or from baby’s side (tongue tie or clenching for example) that causes latch issues. It’s a shame people have to find out by trial and error (mostly error) that it isn’t always easy to follow the steps of this dance especially in the beginning. It is learned behavior, it isn’t innate. If the latch turns out not to be a simple problem to solve, and it doesn’t get better by tomorrow, call either your local hospital and get an appointment with a lactation specialist; or call La Leche League, they have somebody to confer with everywhere.
My own experience is that pediatricians are less than helpful and verge strongly on entirely ignorant in matters involving nursing; but it is my hope that this is not universally true.
Congratulations. And good on you for having the good sense to ask.
For pumps, this early in the game I would rent a hospital grade. Especially with a first baby, you don’t know yet how well pumping will work out or how much you will need it.