Cannot stop gaining and binging after weight restoration

I'm sorry you are getting negative feedback from your family. Everyone should complete withhold comments on weight and think "HEALTHY". Shame on them.

Do you exercise at all? I imagine you have very little muscles because your body burned all of it's fat stores and had to consume muscle. Find some proteins that you really enjoy (nuts, nut butters, seafood and other meats, legumes/beans) and try to get 1g per LEAN pound of body weight every day. Which for you would probably be almost all of your weight - aim for 80-90grams.

What are you binging on? If it's high sugar, simple carbs, they will do that - they actually have addictive qualities and it will take a few days of little or no processed carbs to get over that.

The protein and healthy fats will help keep your blood sugar stable throughout the day and you'll be less likely to binge. You can also get in the habit of having a glass of water every time you want to eat something. Tell yourself you can eat something in 10 minutes. Have the glass of water and go do something. If you are really hungry, in 10 minutes you can have something. This will train your brain to know that you WILL have food - don't feel deprived, just wait 10 minutes. Be OK with a little hunger.

Keep seeing both your doctor and your psychiatrist to address the emotional and psychological issues that are heavily influencing your relationship with food and your body.

Do you have body dysmorphia? If you can be honest about your looks (or even get a friend to help) find a photo in a fitness or health magazine of a body that you think is attractive. Have a friend take a photo of you in a similar pose and attire. Put them beside each other. Your friend can help you see that you probably have a lot of muscle to build but not any fat to loose.

This is why your doctor is concerned. Putting on some fat is good! You need to be about 20% body fat to look your best. But muscle tone is important to make pretty body lines. It is also very dense - much denser than fat. So a very fit, thin person can weight 20 pounds more than someone such as yourself but actually wear the exact same size while someone with very little muscle tone can be "skinny fat" - be flabby while still being in a relatively small clothing size.

Ask your family to stop commenting. Remind them that you struggled with your weight and body issues before and really need to focus on being in good health!

My mom is starting to comment that I am getting "fat" again. However, I find it impossible to control my diet because whenever I try to eat a little less I get a strong feeling of "desperation" and binge the next day.

I can't believe your mom would say that to a recovering anorexic. Horrible.
That said, the best way to feel full on less food is to eat a lot of vegetables, some meat, and very few carbs. Sometimes I make myself a giant salad with Newman's Own low fat sesame dressing, a whole bag of arugula, and chopped veggies of all kinds. By the time I'm done, I'm sick of chewing without having eaten too many calories. Throw in some hardboiled eggs or chicken and you won't be hungry for a while.
Know that carbs, delicious and wonderful that they are, rarely satisfy.
Finally, accept the fact that you may just have to be 100 lbs for a while. It's not the end of the world. I bet you will look quite nice at 100 lbs and feel better too. Honestly, BMI is not good for short (or very tall) people.

Seriously, do these people look fat to you?

http://www.mybodygallery.com/search.html?gender=female&height=150&age=any&weight=45&pantSize=any&shirtSize=any&bodytype=

The binge eating is your response to the severe restrictions you had in place when in the throes of the anorexia. Your mind/body go into panic mode when you even think of trying to restrict so I think that for now, you need to keep any ideas of restriction and keeping to specific calorie goals out of your mind, and instead, aim to eat healthy, balanced meals and snacks when you are hungry, including a treat here and there. Your health is far more important than what your family might think, I am aware it is the culture in some places to comment on weight etc quite bluntly.

I do not know why you are gaining, it could be water retention, some of it, and certainly, simple carbs/junk food does tend to put on weight a lot quicker, I have noticed, than more nutritious foods, maybe because it does tend to also cause your body to hold more water.

I would honestly stop counting calories for now, and focus more on trying to listen to your body. Also, look into weight training/strength training of some kind as for some, that is the way out of the eating disordered chaos...it gives a different focus and will also help build you some muscle mass which in turn will help deal with your metabolism, which probably has taken a bit of a hit.

1. Why am I still gaining weight on 1200-1500 kcal a day? I am gaining at least 1 lb per week. Have I permanently compromised my metabolism from food restriction and excessive exercise?
2. What should I do to maintain a healthy weight without restricting or binging?

Thank you!

1. It's doubtful. More likely you are underestimating what you eat. 1200-1500 calories is not a lot of food unless you are eating mostly lettuce.

2. You need to deal with your food issues. You may need to seek professional help for this. It doesn't sound like the professionals you are dealing with now are helping, so it might be time to look for someone you "click" with.