***** NOT A TEACHER *****
One term for a very nervous and sensitive person is
high-strung.
Tom: Do you like your boss?
Mona: Not really!
Tom: Why not?
Mona: She's very high-strung.
Tom: In what way?
Mona: Well, she's very impatient. And if you say something that irritates her, she
will start yelling. The smallest thing can make her angry. She's very suspicious. The other day she saw
me talking with someone, so she looks at me and asks "Are you two talking about
me?" Oh, and the other day she went crazy because someone accidently spilled
some coffee on her desk.
Edit: I started typing BEFORE I saw Soothing Dave's excellent answer,