Oops, I created a very similar post as this...maybe delete it if you feel necessary but I left my post open to any mental health issue, and started off with a character (based on a real person) living with schizophrenia. You're welcome to reply to that!
Anyway! As far as anxiety only...man, there are so many. Honestly the one that really comes to mind is J.D. Salinger's Holden Caulfied from 'Catcher in the Rye'. He is never explicitly diagnosed with any mental health issue, but it is clear by the time you finish the book (NO SPOILERS AHEAD DON'T WORRY) that he has been in psychoanalysis for his issues and that telling his 'story' in the form of the book is part of his therapy it seems. Salinger himself was a very interesting guy who dealt with a lot of issues, for instance if I remember correctly he was with US forces liberating one of the German concentration camps in WWII. So he saw a lot during his combat experience, and I think he wrote himself as a way to deal with that trauma. One way or another he is Holden Caulfied, or the other way around, and a lot of readers, myself included, really identify with Holden Caulfield. Plus, he's really funny and the book is very poignant.
The Cather In The Rye is one of my favorite books ever.
The movie "Girl, Interrupted" (I have to issue a huuuuge trigger warning for this movie, just.....watch at your own risk) is one of my favorites. Lisa (Angelina Jolie) was just.....omfg.....she was a psychopath in that movie, and she was scary as fuck. She was scary. Susannah (Winona Ryder) was pretty awesome as well lol. She reminds me a lot of myself, actually. she was diagnosed as being borderline in that movie. I've been diagnosed with the same thing.
The film ' Vertigo ' had the lead actor with agoraphobia. His problem was not that he could not leave the house. He felt dizzy when he went up heights. In the film he told everybody about his condition. I just think very little was known about agoraphobia when the film was made. He would be in crowded places all the time. Not a bother on him at all. It was laughable.