Going out of your comfort zone means your body is gonna respond as in any other dangerous situation. The respond to stress in these situations is fight or flight so, your body needs to be ready and in this being ready, feeding doesn’t fit with it.
So, what could be the solution? In my opinion the only way is to convert these moments you have to face to more frequently that are outside your comfort zone into habitual. It takes time, patience and the will to repeat them.
I have a nephew with Asperger’s syndrome and I’m myself social awkward. It’s not easy.
Are you attending to a psychiatrist or a therapist who can help you with anxiety and work on these social interactions?