Fast metabolism problems

So I have always been underweight due to my fast metabolism I can't gain weight properly without loosing all of it.

Last year I went vegan and lost a lot of pounds because I wasn't eating enough I weighed 92 at age 14 5"7.

Now I'm still not eating well because its hard for me to. I constantly feel like I need fatty food. I now have lost 5 pounds in one week and weigh 106. I keep accidentally loosing weight and it unhealthy since I'm very much underweight! I have no clue as to what do. I just moved so My doctor is 6 hours away. I can literally see part of my ribs and my ribs hurt. How do I maintain a healthy diet and weight?