I'm looking for a word to describe someone who is sensitive to the point that other have to tiptoe around her. In other words, someone who can't handle routine jokes, normal criticism, or a comment that can possibly be interpreted in a negative way, even when it wasn't meant like that.
Someone who is hypersensitive is often said to be thin-skinned.
The first word that springs to mind is touchy.
Highly strung perhaps?
edit: Admittedly this is not a single word.
I can think of irascible, which conveys the sense of being extremely easy to anger.
Consider nervous ("Easily agitated or alarmed" and "Apprehensive, anxious, hesitant, worried"), or in the UK, nervy ("Feeling nervous, anxious or agitated"). Also excitable, edgy ("nervous, apprehensive"), uptight, jumpy, sensitive, fragile, delicate.
Edit: Neurotic, typically negative in connotation, is used informally to mean "overly anxious".
Perhaps the word you are looking for really is "sensitive":
excessively affected by external agencies or influences.
easily pained, annoyed, etc.
What about "susceptible"? I think il fits the sense that you have expressed.
Collins English Dictionary defines "susceptible" as follow: "easily impressed emotionally".
Also, Oxford Advanced Learning's Dictionary defines "susceptible" as follow; "easily influenced by feelings and emotions", ("She was both charming and susceptible.")
In the vernacular, someone who is hypersensitive could be called a: