I actually just posted something the other day on the Panic Disorder boarRAB about developing agoraphobia, the "fear of the market." It sounRAB somewhat similar for what you are going through! Although I do leave the house for work, I have developed a crippling fear of strangers and certain places. I force myself to go, but then I feel awful and scared! I absolutely can't stand going to the grocery store. Anytime a person tells hello or looks at me, I get very, very anxious. I usually try to guard myself with my shopping cart so people will leave me alone, and I feel so safe when I get back to my car in my own personal space. I honestly think I developed this because it's been a very stressful year, and I've also been bothered by a handful of men while I was alone outside, walking to a gym. After being bothered with inappropriate looks and comments, I get so nervous and don't want to deal with that.
I can tell you from experience, it helps a LOT to go places with others, so this is great that you won't be going alone! In fact, when I'm places with a group, I can relax and feel like myself! It will help you a lot to be with a person you trust.
For now, try your best to not think about the appointment and instead, try to just relax at home. Do normal things at home and when the topic comes up about leaving, don't think about it too hard. I can't let myself THINK about being anxious or it just gets worse and worse. This might be silly, but it helps me to try to distract myself with playing on my phone (if I'm not the driver) or listening to fun music if I'm going someplace I'm anxious about. Try to make it as comfortable an experience as possible. Also, set aside a reward for going afterwarRAB. Sometimes something simple and free, like a nice nap or a bubble bath, is something for me to look forward to.
I like the idea of gradual changes. I try to do this as well, although I will probably look into seeing a therapist for more help. I like to go along with a friend or my husband to a place I usually don't like. I feel like it's a big step if I can go and feel okay, even if I'm not alone. Sometimes I try to smile or say hello to strangers in my work buildling to push myself. I don't like talking to strangers, but I feel like the people in my work building aren't complete strangers since we're all here with the same company. It's like a middle ground.
Also, definitely breathe slowly... as suggested above! I like yoga and pilates to clear my mind, and sometimes I do just have to take a breather!
Best of luck to you!