I think you may want to ask yourself what you would do with your pet, assuming its not a fish, if you had a roomate or hallmate who had allergies.
I am very allergic to dogs...my eyes swell shut in about 30 minutes......If I have a choice between anaphylactic shock and putting your dog or cat on the street you know my choice...I think the school would agree.
My reply assumes you are going to be in a dorm and you are not bringing a fish. Turtles you have salmonella. Birds....well I'm allergic to feathers to but I love chicken. Pets would make great practical joke targets. I can just see a blue poodle with pink poka dots after some clandestine chemistry lab experiment.
Seriously I think you will have enough to do without a pet. Wait until you have some private space. My sister was in a dorm for her first two years. As a junior one of her friends got a dog. They are in an apartment. Someone always had to stay in town to watch the dog walk the dog feed the dog get the picture. they love the dog but its a real burden on their social life
Now snakes that's another story.....messy roomate....crumbs on the floor and after a month or two mice...you know those old 50's style dorms are not exactly air tight. Nice snakey poo problem solved. Snakes you may be able to get by with one of those.