Have you asked if you could install a room air-conditioner? I’d try that first before making a drastic change. You might be able to make a medical case for it, since cystic acne is not just a cosmetic problem.
But if you do decide to apply to Wellesley and get in, ask to live in Dower. It’s not a popular dorm, but it is very quiet. My daughter lived there her first two years and loved it. No A/C though.