I don't mean to be a buzzkill, but I just looked up your weight loss goal compared to your height and found that, at your age, you would be thinner than 97% of the women in your age and height group. That seems like a lot of pressure to put on yourself. Were you at 110 lbs. before without a lot of food monitoring and with moderate exercise? If not, it may not be reasonable.
I humbly suggest that you try to let go of your weight loss goal for now. Weight loss goals have not been shown to be effective incentive to reverse binge eating disorder; in fact, just the opposite. Concentrate more on committing to weaning yourself off overeating for now. It is much more likely that you will be successful in the long run if you work at REDUCING the amount of food at and the frequency you have these episodes. This will not happen without some tolerance of discomfort! Really, almost no one goes from bingeing to not bingeing overnight- and staying that way. Ditto for ditching sugar, wheat, or carbs permanently, no matter how much attention is given to the few who do. Don't bet on terrible odds! It just leads to likely failure and a loss of self-confidence. Plus, your THOUGHTS about what you're doing-- esp. when you fail- that are the real battle. Let us hold your hand while you go through this process. It will probably take longer than you wish it would, but together we can get through it!
BTW, just for a little hope, I have reduced my weight by about 20% over the past three years, and I started increasing my pleasure in eating almost immediately. I'm about back to what I weighed when I graduated from high school in 1971!And before my first official diet. I wish I had never started dieting! I wasn't sure I would lose weight but I did know I absolutely needed to reduce bingeing after 38 years of problem eating. I've lost more each year, but with a downward TREND, not in a straight line. It is worth it to be patient! 1240 days ago