It is going to be a part of your thinking for a while. It takes time to become an alcoholic, so it shouldn't be terribly surprising that it takes time for the thoughts and habits to fade. They become less and less frequent, and one day it will occur to you that you haven't thought about drinking for awhile. Most importantly - when the urge to drink comes on (and it will in the early days, part of the process) do whatever you need to do to not drink. Run, call a friend, go for a drive, eat some ice cream, watch a favorite movie, whatever.... usually the thoughts and urges only last 15 minutes or so and start to fade. Just hang on, grit your teeth, and don't drink. It is in those brief periods that our drinking brains go into overdrive, and then wear themselves out. It's not fun, but it's a whole lot more pleasant than relapsing. Eventually, being sober will be your new normal and you won't see your life as an endless battle against your addiction. Just trust the process, and let time do its thing.
Good luck, you are exactly where you should be.