Wait at the door a minute, until Einwyl collects herself or the time finishes, and then walk in, asking, "Einwyl, what work I do?"
A combination of your two ideas Nature and Super.
Eiwhyl lowers her head and hides it behind her palms, her arms resting on the counter, as if the argument somehow physically exhausted her. After a few seconds of this she gets up with a sigh and looks around. That's when she notices you. She whispers something to herself and then motions for you to come.
"Well, don't just stand there! Come in!"
You slowly and carefully walk inside, making sure to remain aware of where the door is at all times, so you can make a quick escape if necessary.
"Eiwhyl, what work I do?" you ask.
"Well, that's the question I've been asking myself all the damned day today, trying to pull something outta my choobies. What in the void is a dragon supposed to do, of all the blasted things? You're supposed to be stupid beasts or mythical creatures. Why aren't you off... I dunno, hanging out in an asteroid, giving out quests to spacers or something? What are you doing in my city?"
You're not exactly sure what she's asking or why she's mad at you, so you stay silent. Eiwhyl stares at you for a second and then sighs, seemingly much calmer.
"I can't believe I'm saying this, but you can help around here, I suppose. I could use someone to keep an eye on things while I sleep. I've been looking to hire another nurse ever since Iseng'ela run off, but well... you'll do." she says with a dismissive wave of her hand.
"It'll help you avoid attracting too much of the wrong attention and it will let me keep an eye on you and make sure you don't do anything too stupid. What do you say? You're up for that?"
You don't know what being a nurse means, but you could at least try to help Eiwhyl. She'll probably teach you what exactly that entails.