I'll start with saying that I have never suffered with anxiety but I've had my share of fear and sadness.
The strangest thing is when a client sits opposite me and tells me about their problems, problems very familiar because I'm going through it myself. This has happened to me dozens of times and it's difficult, let me tell you. I never tell clients about my life, this is their time and anyway, it's not on them to solve my problems! It's the last thing a therapist should do, even when people ask. Clients come through the door and politely ask 'how are you?'. The answer is always, 'Good thank you!', whether I'm falling apart or not (I haven't fallen apart yet!).
A good therapist has a change of gear, a moment where you pull down the shutters on yourself and and focus on their client, no matter what is happening- a struggling relationship, a death in the family or something else. It's a shift in focus, I think. In a previous life, I was an actor and I had the same thing then. Whether I was a stinking cold or emotional pain, there was a show to do. I've stood in the wings of a theatre loads of times and had to take a deep breath before stepping on stage. Being in a comedy was the most trying. Just for an hour or two, the pain always seemed to disappear.
Anyway, therapists are human beings too, that's why so many of us have therapy ourselves. You shouldn't ever get even a hint of this, if you do, I've let you down. I'm grateful that I'm pretty chipper most of the time, that I don't suffer from anxiety or depression. I get down sometimes, but when I do, you'll never know.