Hello!

I am just starting to learn Chinese, and I just learned how to say what I eat and do not eat. I am planning to travel to China in a few months, and I have a specific diet. Is there a shorter or easier way that I can say I don't eat meat/dairy/eggs, or that I need gluten free options? I know this can be a real pain, I just want to make sure when I order that I am doing it in the best, most polite and correct way. Please if you have any tips let me know. Thanks!