Advice: ED recovery and metabolism

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Hello everyone.

A bit about myself: I've always struggled with body image issues even though I've been thin my whole life. I am 19 now and when I was 17-18, I had always weighed about 113 pounds. I was happy with that and my weight pretty much stayed there. However, I went to university in the fall of 2013 and I had started to gain the "freshman 15." By December, I weighed about 121 pounds. So I set out to lose those pounds that I had gained since coming to university. Simple as that. So I started losing them. And losing more weight. And losing more weight. By June, I weighed 100 pounds. I didn't really realize that I had an eating disorder until I critically examined by attitudes and thoughts. As of right now, I'm 19, 5'6, and weigh about 100 pounds. I also haven't had my period for 3 months.

So I've undertaken a mission to gain weight. However, I really do not know how to go about doing this healthily. You see, I'm scared that when I start to eat more and consume more calories, my metabolism will go crazy and I'll just gain excessively and also gain fat. So how do I gain weight where my metabolism will remain normal? Also how do I primarily gain muscle and not fat? See, I'm terrified of gaining body fat. I only want muscle, not fat. Now I know I will gain fat when I gain weight since it's only natural but I just don't want to gain too much fat.

How can I gain weight and make sure that my metabolism stays normal? Should I gain like 1 pound a month? My BMR is 1224 right now. How much should I increase by? 100 calories a week maybe? And how can I ensure that the weight gain will be muscle in addition to fat?

Thanks so much everyone.