work up？

It's "worked up" and not "work up".

To get "worked up" over something means to become overly emotional, or overly upset, or distraught, in response to something that is frustrating you and not going the way you want it to go.

In your example, the pediatrician is overly emotional about the fact she has difficulty nursing her adopted baby, even though she tells her patient's mothers to remain calm, or not get overly upset, when they have similar difficulties.

upset, crying, emotionally disturbed, angry, irate, grumpy, jelouse.
Anything to do with an undefined heightened emotional state.

We can infer the particular emotions from the context of the passage.

As FireFly said, it's 'worked up because it's a passive construction,

be/get worked up by something

A 'work up' is, I believe, what doctors might order for a patient; a complete work up would be an extensive series of test to determine some unknown malady.