THIS is a great question and first of all, I'm sorry that you aren't able to eat some of the things you like π BUT, I'd love to help try to make your life easier when you're living in Korea!
First of all, I would suggest you carry around a paper (maybe laminated) that lists all of your allergies with: "μ λ μ¬ν (insert thing here) μλ λ₯΄κΈ°κ° μμ΅λλ€. λ¨ΉμΌλ©΄ μ£½μ μλ μμ΄μ μ‘°μ¬ν΄μ£ΌμΈμγ
γ
."
This sentence means "My _____ allergy is very severe. If I eat it I could die, so please be careful" While it might sound quite extreme to write this out and carry it around, I think that it's always better to be safe than sorry and some people might not understand the severity of certain allergies so this is just a precaution!
Secondly, I'd recommend checking out some vegan or gluten friendly restaurants! I know there is one in the Itaewon area called SunnyBread :) But I'm sure there are more online β€οΈ | 
