sorry you're experiencing this! I guess I would say to just tell your walking partner that you have anxiety. The small chance they try to dig for more information is small, but if that happens just say "I'd rather not talk about it". Or whatever. Most people would be fine with "I have anxiety" and you won't need to explain yourself further. I think doing that will help the situation because then you won't feel as self conscious. Now you are feeling anxious about appearing anxious. Just don't give up on it because it's too hard! The more you expose yourself to your fears, the smaller less powerful they become. Good luck!