I am sorry that you are being forced to go, however if there is no way around it then we can think of some coping mechanisms to get you through this time. I still think it would be great to chat to the year coordinator so as that they are aware of how you are feeling and that they can just be mindful of you and keep an eye out for your wellbeing.
It is good that you can identify why it is that you don't want to go to camp and being away from your family is pretty common. There are some ways to help with that and you might think this silly but I will suggest it anyway, you could ask your family to make a little book for you, and each day you can read a page that they have written to you and maybe put a photo in there to look at, something from home to look forward to each day to read and to make you feel safe. A small book could be put into your bag so as not to draw attention to you feeling homesick.
The food is usually pretty standard stuff like spaghetti bolognaise and lasagne, perhaps they might do a BBQ, I think as long as it is hot then you are going to be pretty safe with the food. They do cater for large amounts of people at camp and usually get it right as they really cannot afford to have a camp full of sick people so hygiene is pretty paramount.
The vomit part seems to be very traumatic for you and I know you only have past experience to go on, but can I suggest that while yes, people do vomit at camp, it is usually only one person or maybe two, does this make it easier no it doesn't, but I think trying to let yourself know that it is probably not going to be a daily thing, and it perhaps may not happen at all. It is very traumatic for you so in the instance that it does happen I think removing yourself from the situation and perhaps finding a friend or someone who you can be comforted by would be good. As much as you are thinking about it happening, perhaps trying to think it also may not happen too and give yourself some peace from that panic, as it really may not happen and you have been through all that anxiety for nothing.
I think thinking also of the good things that will happen, the fun activities, the times with your friends, you might have a movie night, there will be lots of fun things so try to make a list even of some of the good things that you know you will enjoy.
I am not sure if I am helping here, but talking might just help too.
Huge hugs to you