I taught in Korea for four years and it always irritated me, too.
If I took something, it was commentary on how much I liked it or how well I could eat Korean food.
If I didn't take something, it was commentary on how I couldn't eat Korean food. Not only do they talk about you in English, but they talk about you in Korean as well.
One day I was feeling sick and wasn't up for fish with fish soup and kimchi---since that DOES comprise practically every meal, and isn't so easy on the stomach---so I just ate rice and broth. My coteacher concluded that foreigners couldn't eat kimchi, even though I had eaten in that cafeteria loads of times and had been in Korea for a lot longer.
Food nationalism is just something you deal with in Korea, and as you may or may not have noticed, all textbooks have a chapter on how spicy Korean food is and how foreigners have a hell of a time with it (or can't use chopsticks). Even in Korean-language books, for foreigners learning Korean, the example sentences often revolve around food difficulties.
At times when I wasn't in the mood I just skipped lunch, brought my own, or went to the kimbap shop across the street. When I did eat in the cafeteria and the commentary became too much, I just ignored it. Trying to explain yourself to Korean-speakers can be tough, and can feel a lot like Groundhog Day, because it'll just come up again the next day.
Try mentioning to your co-teacher how you feel, too. Make sure she knows you're a vegetarian, and maybe say that you're trying to adjust to Korea but constant attention is making it difficult at times.