It bothered me when I was newly sober and still coming to grips with it. Now at 3.5 yrs sober I have been told by several people that they have never met someone who can be so open about it. I don't shout it from the rooftops but I do acknowledge it, I accept it and I try to educate about it when possible.
If you are just in the very early stages, which it sounds like you are, don't worry about it. I'd say it's normal. You just try to focus on getting and staying sober and don't worry about what anyone else thinks about it besides you. There are numerous ways to decline a drink without screaming I'm an alcoholic. When you get ready we can help you out with that but I'd be so bold as to say you might want to put a serious curtail on the socializing until you get yourself dried out and some recovery tools under your belt.
Anyways, that's probably way more than you were asking but I do hope you will find it helpful. I will say one more thing. I was not your classic vision of an alcoholic either. I went from hardly ever having a drink to black-out, physically addicted, couldn't go more than a couple of hours without a drink or I'd shake to death in 3.5 years start to finish. Getting sober was the hardest thing I have EVER done and going through the withdrawals and stuff is something I hope to never have to do again and I have nothing but the greatest compassion and hope for those who can face those fears and go through it. I promise you life is SO much better on the other side.
Hang in there and hang on to us, you're in for the ride of your life!
Hugs,
Kellye