I experienced the same questions and issues when becoming sober...
There is a book I was given early in my sobriety titled "Living Sober." In that book it says the following which is relevant to your question of what to tell others and what they will think when they learn you are not drinking...
"The newly sober alcoholic wonders what to answer if drinking friends and relatives say such things as 'come have a drink.'; 'What are you drinking?'; 'Why, you can't be an alcoholic!'; 'Don't you drink?'; 'Just one won't hurt.'; 'Why aren't you drinking?'... and the like. To our relief, we found that these questions come up less often than expected, and our answers seem to have much less importance than we thought they would have. Our not drinking creates less of a stir than we feared it would."
Living Sober then later explains that you know you best and "your own intelligence will lead you to the one [answer to why you are not drinking] that works best and is most comfortable for you. More importantly, you should not feel the need to defend ourselves and our choice to not drink.
The book recommends some simple answers to the above examples of questions such as: "I am not drinking now." or "I am not drinking today (or this week)." or the most simplest form being "No thanks." or a more straight forward "I don't care for any." ; "I've had my share."; "I've had all I can handle." ; "I found it doesn't agree with me. These can all be truthful answers.
Although, I along with many others would not recommend being untruthful because honesty is a big part of sobriety I personally when the question of why I am not drinking would recommend simply tell a little white lie such as "I am allergic." Just be careful not to make a habbit of using this as an reason for not drinking if you personally feel like you are telling a lie when you say it. But in reality... when you really think about it - Alcohol IS REALLY a allergy which is a "disease" that us Alcoholics have. Our bodies and our minds do not react the way others who drink alcohol do. So, if you are faced with having to tell someone you are allergic to alcohol - rest assured you would not be the first to do so.
I wish you the best with your sobriety and just remember to take things one day at a time and quite simply dont drink
