Hi Amanda,
First off, I believe that your dog is concerned about you because I think our pets understand the pain we are feeling. And, your dog does need you to be the best you can be.
And, I agree that stopping drinking could help your depression to lift, if you give a little time.
It might be a good idea to step away from your family for awhile and work on your recovery and other parts of your life. I know it's hard, but take small steps and you will see things begin to turn around.