I'm guessing you're allergic to something in your room!
Given that you're okay at home, try thinking about what the differences are between your room at Uni and your room at home. General cleanliness? Different cleaning products used? Differences in bedding? Laundry powder? A saggy old mattress? An air freshener? Figure it out by a process of elimination.
Generally speaking, someone with eczema will need to stay away from synthetics and harsh chemicals. Natural fabrics (100% cotton sheets, for example) and products are a better way to go. You might also want to think about getting anti-allergen duvet and pillow covers if dust mites are the problem.
Sounds like your allergic to something in your room
Is the washing powder same as at home?
Does the area have different plants?
Try an antihistamine see if improves, if it does try removing and figure out what it is your allergic to if it doesn't I'd see a doctor?