No, you're not blowing it out of proportion. OTOH, you are the one with the drinking problem, not her. She was insensitive (to put it mildly), but she didn't make you drink. You must realize that.
People who are not alcoholics (or people who are problem drinkers that feel threatened by someone else's recovery) don't "get it" why we can't drink. She either wasn't taking you seriously or she was deliberately out to sabotage you.
I think I would avoid this "friend" now that you are committed, again, to getting sober.
Do you have any outside support? I found going to AA provided a great network of sober friends. AA is much, much more than fellowship, but the social aspects are very helpful when you are newly sober.