Dr. Clay is the doctor who helps Ma and Jack readjust (or, in Jack's case, adjust for the first time) to the Outside world. Noreen is the nurse who carries food trays and watches over Jack and his Ma. She seems to act more as a maid than as a nurse in this special circumstance.
Dr. Clay makes Jack his first priority. "The immediate priority is to help [Jack] feel safe. Both of you, rather. It's a matter of slowly, slowly enlarging the circle of trust." (4.380) He practically pencils Ma in as an afterthought there. Her return to the world is taken for granted, which might just be one of the reasons it's so hard for her.
While he's primarily their healthcare provider, Dr. Clay doesn't just give Jack and Ma shots—he also quotes poetry. He says, "World is suddener than we fancy it," (3.579) a quote from Irish poet Louis Macneice's poem "Snow." He even hits the classics with quotes from Emily Dickinson—"The Soul selects her own Society—Then—shuts the Door" (5.985)—and T.S. Eliot—"Human kind cannot bear very much reality" (5.353). How did this guy have time to get through med school and memorize verse?
We guess that Dr. Clay specializes in treating both the mind and the soul. Speaking of soul, he doles out that Emily Dickinson quote like he's writing a prescription to Ma. She's frustrated that she's changed, and he's basically saying: of course you've changed in seven years. And it's okay to want to spend time with your son and only your son some days.