I truly think there is a thing. Yes.
The fear of fear? Hmmmmmm
Probably .... People can fear just about anything. Fear of fear sounds like a paralyzing double whammy!
Feeling anxious is not particularly pleasant in and of itself, so it would seem if one has a history of being anxious as a response to various situations that one could rightly come to fear that they might become anxious.
Fear relates to a known or understood threat, whereas anxiety follows from an unknown, expected or poorly defined threat.
Fear and anxiety often occur together but these terms are not interchangeable. Even though symptoms typically overlap, a person's experience with these emotions differs based on their context.
(An aside: Agoraphobia can progress to a "fear of open spaces"---which is the definition I learned many years ago for that word. I would suggest you reflect on the two words, fear and anxiety, before you start using "agoraphobia" to refer to a fear of anxiety.)