Hi Angie,
I find that keeping busy is really helpful as a distraction from drinking, but I find that I also need to "work" at it. By that I mean, coming here and posting on SR, reading books on alcoholism and using strategies that are "out there" (eg/ cost-benefit analysis, listing why drinking for me is worse than not drinking, etc.) Some people get much support from attending AA.
I think it is quite common to slip, especially at the start (I know I did, a few times) but if you're determined and you surround yourself with support and strategies, eventually your days string into months and years. Just one baby step at a time...
Hugs,
CS