I would venture to say that the incidence of psychological issues is about the same in the profession itself as it is in the general population. The difference is that any well trained mental health professional confronts, treats, deals with self issues, through training and supervision, as well as personal growth. It would be hypocritical of the professions, to reject or no support colleagues with issues or medical problems, like an us-them divide.
Suffice it to say, that I have seen psychiatrists and mental health admins, who, behaviorally, appear to have personality disorders, which, they inflict upon others, and due to power, get away with it. Narcissism is the biggy.
So, as panic disorders and speaking anxiety, are probably more responsive to treatment, than other things, I say, go for it. You would probably have a more empathic understanding of these and able to help clients who deal with these. How likely are you as a future clinician to have to address large audiences? Probably not much, so stay out of admin. If you do well one on one with clients, you should do fine. Get whatever help you need yourself, and then go for it. Heck, Freud was a cocaine addict. Many others issues pale in comparison.
So I'd encourage you to continue considering clinical training.