IdiomCenter.com

I have this thing about something, as in "I have this thing about bed bugs when I stay in hotels. I get all itchy just thinking about them." (Mike)

a hang-up (about sth) (a permanent and unreasonable feeling of anxiety about a particular feature of yourself):
sexual hang-ups
He's one of these men who went bald very young and has a terrible hang-up about it.

hung-up (having a hang-up):
Why are so many women so hung-up abou

have a [bee in one's bonnet]

See also
[have a screw loose]
[тараканы в голове]

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chaika

I think Mike's suggestion is best, in the sense that it is a word that one would apply to oneself, whereas nobody would say they have a hangup about smth. You can never see your own issues. All the other words are what you would use about somebody else. =:^0