It is horrible. Really horrible.
I've not got much advice as I'm going through similar. I really thought I was having a breakdown a few weeks ago.
There's just no break, no rest, it's constantly busy. We've got no outside help at all, and we have huge stress in terms of work/money at the moment. Coupled with no sleep for over 2 years, I'm falling apart, but still having to work (self employed).
I do totally understand letting people down. I cried during my mini breakdown that I was letting my children down, and that they didn't deserve a mum who didn't even have time to play with them. Worse. Didn't want to play with them 
Relaxing is very hard for me, I can't switch off. But I am trying.
Just don't bottle it up. You're doing the right thing, going to the doctors etc.
People might talk at work, they might not. Unless they're friends, don't give them a second thought. If they are friends, then they shouldn't be talking about you badly behind your back.
Concentrate on you and getting well again, and keep seeing it as a physical illness. If you had the flu you wouldn't feel guilty, as you can't help being ill. Well, you can't help this either.
From someone who has coped through some very very difficult times, it's hard to accept I'm not invincible. Admitting I'm not strong enough is hard, but we all have our breaking points.
Hope your doctors appointment goes well today. Tell your DH you feel like you're letting him down (he'll reassure you that you're not). I did this with DH a few weeks ago and it was good to get it off my chest, and for him to understand just how low I felt. It wasn't just a one off bad day.
Unfortunately stress and anxiety can spiral quite quickly. Wishing you lots of luck and hope you get through this soon x