Hi bluegem, tough spot to be in at 3 weeks sober! But if you have to go then it's best to go prepared. I agree with what the others have posted here, drive to the wedding, volunteer to be a DD or to run some kind of helpful errand for the newlyweds that will keep up your motivation to stay sober. Write down some phrases that are helpful to you. Call a sponsor or trusted friend if you feel overwhelmed. Scratch that, LEAVE if you feel overwhelmed, cough, cough, you're sick and can't stay, much love, peace out.
I was pleasantly surprised at how little anybody cares that I'm not drinking. The vast majority of people don't notice or care because they're not obsessed with alcohol like we are. The few people in my life who noticed I wasn't drinking were heavy drinkers themselves and passed no judgment, they actually said they wished they could quit too.
Just remember, you don't owe anybody an explanation! And you probably won't be pressed to give one. But it will make you feel better to have one at the ready, as well as a getaway plan.
Best of luck to you, stay strong, do what's best for you in the long run, remember, a true friend loves YOU, for who YOU are, even if that means you had to leave her wedding early to protect your sobriety.