Usage patterns
〈事〉に神経質になるto become nervous/overly sensitive about something
He's become very nervous about his health lately.
〈物〉に神経質だto be fussy/particular about something
She's very particular about dirt in her room.
〈人〉は細かいことに神経質だsomeone is fussy about small/minor things
My department head is fussy about the smallest details.