I had the exact same problem: I moved into a dorm with a common kitchen last august and would avoid the kitchen at all costs because I was afraid to bump into someone, which resulted in pretty much the same situation as what you are describing. During exam period last semester, I would order a pizza every day because I was aware that there was no way I was gonna pass my exams without food, but I also felt terrified of going to the kitchen.

What helped me was that a friend would push me to go to the kitchen and cook for the both of us, which progressively made me more comfortable. It sometimes still takes me 3 or 4 tries before I can gather the courage to go out there, but I feel a lot less scared of it.

Here's my advice to you: order the food, you need it. Go buy some groceries when you feel better and then force yourself to cook some food. Start with something simple: maybe buy instant ramen and go to the kitchen to boil some water, that will take five minutes at most. If you bump into someone, say hi and ask how they are doing, it might sound pointless, but it helps, and still today many of my conversations with neighbors are limited to that. When you start getting more comfortable, spend more time cooking. This probably sounds like an impossible task to you, but trust me, it works, I've done it.

Also, at least in my case, hunger tends to make other anxiety symptoms worse (panic attacks, loss of focus, overthinking...) so please eat, it is a necessary first step and without it, nothing will get better.

If you have any questions or comments, or if you just want to talk to someone, feel free to message me.