Paranoid should work here.
Unreasonably or obsessively anxious, suspicious, or mistrustful (Oxford)
I hope I'm correct in assuming that you want a word which describes the nature of someone being worried easily, not a word to describe their current state of worry.
I hope my mother doesn't find out how risky this is, she's paranoid. = (She's not worried right now, but she will be if she learns of this; that's her nature.)
EDIT: As is common knowledge, I hope, the word paranoid refers to a mental disorder in its primary sense. However, its usage in the metaphorical sense is quite common, and doesn't necessarily imply that you think she suffers from this illness. (English is littered with metaphorical usages of medical conditions, with varying degrees of social acceptance: "Are you blind?" "Are you deaf?" "Are you insane?").
The more noteworthy thing here is what @Peter points out in the comments: that the word is also used metaphorically in a different sense -- to suggest a fear of persecution.
In any case, like thousands of other words with multiple meanings, I don't think you'll have any trouble getting your meaning across, given the proper context.
I advise the detractors to familiarize themselves with the concept of Etymological fallacy.