Maybe she thought she was doing you a favor, getting your results faster than the lab would give them to you, but she's showing you she has no concept of normal boundaries.
You seem like a kind person, but I don't think I could stay friends with this person after that (regardless of her need for a good, understanding, caring friend in her life). I mean, really, now this "friend" has your private info, which she could use poor judgement in distributing it to other mutual friends, etc. I could understand how upset you must be. Regardless of what "personal info" she has, and regardless of whether you call that laboratory and report the violation, I would probably just do a quick fade on her, like not answering her calls, having other plans when she wants to get together, etc. Whether she comes to the conclusion that her behavior necessitated the distancing, is her problem. You deserve to have more time to focus on friends you enjoy. She's not just emotionally fragile, like a wilting flower--she sounds like a china cabinet full of breakables, ready to topple and hurt lots of people/things in the process.
Sorry you had such a bad experience, hope you feel better soon. You certainly did nothing to deserve such heinous, misguided actions from her. I don't mean to diss your friend--but she made a serious mistake, and even if the friendship survives, she created serious trust issues not easily overcome.