Yes, it gets easier! The obsession will fade, slowly but surely. There were lots of times at first that I just had to hang on (coming here really helped). I had to fast foward through the initial temptation to the next morning, knowing that one drink would lead to waking up in misery. And I'd have to face the temptation to drink again the next day and the next. The only way to get rid of the obsession is not to feed it.
Good for you for choosing sobriety when alcohol was right in front of you. That would have been hard for anyone. Stay positive - it really is a great feeling when you realize one day that you just spent a whole day without thinking about drinking. You'll get there........