Best Answer - Chosen by Voters
I'm a recovered alcoholic who had his last drink three years ago on the 30th of this month, so I understand your problem.
Don't fake illness or make excuses or you'll be doing it forever, tell them the truth as you've already put it, you have two choices either drink soft drinks as has been suggested, you may find this boring after a while, especially when you see your friends getting sillier as the time passes.
The other choice is to find another set of friends as I have done, who share the same thoughts and ideals, you can of course mix the two depending on how close you are to your original friends.