Good for you for getting back at it. I hope you can stay the course.
You know you can also come up with other "excuses" rather than saying you are an alcoholic if you don't want to disclose that to certain people. In fact, in making your sobriety plan a good part of that would be how to handle certain situations. I have different responses I give based on the circumstances of the offer of a drink or a gift, they vary depending on who I am talking to, where we are, etc.
In this case you could have said you are an alcoholic and quit drinking or you could have said any of the following:
"how kind of you to remember my birthday! no need for the gift man, really. And actually I'm doing dry January this year!"
"Thank you so much, how generous! But you know what? I've decided to cut out alcohol. I need to shed a few pounds and I am really looking to get healthier this year"
"Wow, you shouldn't have! You know what, why don't you keep this at your house. I've decided to cut out alcohol for the time being but I know the wife would love a vodka tonic next time we come for a visit"