Well done on getting through a whole month!!!!! The good news is that the urges to binge do get better and you'll develop the skill necessary to manage those cravings. A year ago I decided to getting healthy and committed to a complete lifestyle change. The first thing I focused on was my unhealthy relationship with food and my seemingly uncontrollable binging.
Me and food never had a healthy relationship and I dealt with various eating issues since adolescence. When I committed myself to changing my relationship with food and to stop the binging, it was so freakin' hard...there were times where I felt like a heroine addict going cold turkey, needless to say I understand how difficult it can be. The first month was the worst, but it did get better. Of course since I'm human and therefore not perfect I slipped a few times. But the slips have gotten further and further apart, and not quite so bad. The last time I overate was over the holidays and it was on salad (it was pretty much lettuce and salad dressing, and really it wasn't even that much, lol). So it does get better, you just have to keep strong and have faith in yourself.
Also, when I do get the urges to binge nowadays it tends to be when I hit important landmarks (e.g. onderland, reaching 190, 1-year, ...). At least for me, my binging is closely tied to self-destructive thoughts and they tend to get triggered when I'm succeeding. So maybe for you, reaching the one-month mark is sort of similar?
Anyways, losing weight and changing our relationship with food is definitely a journey with ups and downs. It's not fun when everything seems to be working against you, but just know that it will get better. And if the worst happens and you do slip don't let that be an excuse to completely sabotage your efforts. Bumps are to be expected. Stay strong, stay on plan, and you'll be fine.