Are phobias considered anxiety disorders? And should doctors diagnose them before you publicly say it?

Like, I have ornithophobia, a fear of birds. My worst example of it was when I was in NYC once, a flock of about 200 pidgeons flew by, and I ended up in fetal position on the ground for 10 minutes, shaking and breathing heavily. It fits what people describe a panic or anxiety attack as, but I don’t know if it’s the right term, and I don’t want to say I have an anxiety disorder if it’s just a self diagnosis. If phobias are even considered anxiety disorders.

But, do phobias need to be diagnosed? Like, I know I have a fear of birds. I don’t need a psychologist or doctor to tell me that. But I also don’t want to come off as the guy who self diagnosis with anxiety, when I have the means to get an actual diagnosis. Idk 🤷‍♂️