16 year old girl, haven't received period in 6 months

Hi! I'm a 16 year old girl, weighing 133lbs at 5'11. Currently I am recovering from an eating disorder (bulimia with anorexic tendencies). This past year I have lost 30lbs, at the beginning of my weight loss journey (which was healthy at the time), I would receive my period monthly. But after I had lost 10 pounds in the duration of two months (by February) I would stop receiving my period. I haven't received my period in the past 6 months, my menstrual cycle initially started when I was 14 and was regular. I know it is normal for teenage girls to have irregular menstrual cycles but I worry that I haven't received my period in such a long period of time. I went to a gynecologist and my doctor, in my blood work I had no complications (both hormonal and other), the only thing that I don't have much of is iron-but anemia is common in my family history. I no longer am as stressed out as I used to be and I beg my brain to get my period back since obviously it is only very stress related. I have high anxiety which does make me stress out a lot but this has been an ongoing situation since before I even started receiving my period. I also am a sufferer of very intense and painful migraines (dizzy spells, vomiting, confusion, etc) and have been hospitalized 3 times because of my migraines. My migraines proved to be stress related so when I began to relax more I stopped receiving them and now I haven't gotten a migraine for more than a year. In a week's time I am leaving to boarding school in the UK which is far away from home and I won't be living with my family. My gynecologist told me that he would give me time to think about birth control until I came back for holiday break (in late October). However, today I had a check up with my doctor and he urged me to go on birth control even though he didn't really know of many types of birth control. He told me to go on Yasmin, but after further research online I read that majority of people experienced weight gain and higher levels of anxiety or depression or migraines. Because I am prone to all three (anxiety, depression and migraines) I decided that it wouldn't be worth it to go into a new country without my friends and family support on a birth control that could give me these side effects. Basically, my question is SHOULD I try Yasmin? Or should I go with my gut instinct and keep carrying out this "drought"?