Without some kind of healthy fat to add to meals, this definitely won't work for you right now. You would more than likely be hungry all the time and probably pretty miserable.
I see a couple of possibilities here. One, if can you get a fridge for your room, you could get some whole30 compliant fat sources like salad dressings, olives, premade guacamole and occasionally maybe some other food that you could keep in your fridge to supplement what you can get in the dining hall. This would still be pretty boring but doable.
A second possibility would involve talking to the people in charge in the dining hall and seeing if they could make some other options available.
Or, you could decide that a true whole30 is just not an option right now but that you will adhere as closely to the meal template as you can. If you know from your reintroductions that there's something that really, really bothers you, avoid that, obviously. But if there are options that are close to whole30 but not quite -- maybe things are cooked in oil that isn't great, or seasonings have sugar, or they use butter on something -- choose those things.