Touchy

[Sarah]

Peevish; irritable; irascible; techy; apt to take fire.[Colloq.]It may be said of Dryden that he was at no time touchy about personalattacks. Saintsbury.

[Sarah]

A person who:
a)is sensitive
b)takes things personally/literally.
c)a person who can't take a joke

[Sarah]

touch•y/ˈtəCHē/Adjective

(of a person) Someone who is oversensitive or abnormally irritable: “Rusty busted an old man’s hip after he referred to his phone as a toy”.
(of an issue or situation) Must be handled with kid gloves; delicate topic: “Rusty’s phone company placed a data limit on his account”.

[Kit]

When a person [gets] [curious] of something and they [touch it].

[Magaret]

Easily upset or offended; oversensitive.