I was like this too, and I know this is bwf, but powerlifting is what changed this for me. Heavy squats and deadlifts will build an appetite. Satiate it with the right foods, and you will grow. I put in 20lbs in a year after being chronically underweight for most of my life. I was a bit older than you are, though. That might play to your benefit (easier to gain muscle) or to your detriment (youthful growth metabolism), but if you're really keen on it, give it a try. Check out Starting Strength or Greyskull LP (I actually preferred GSLP over SS, but I did SS first).

Something that also worked for me: weigh yourself before bed every night. If you weigh less than you did yesterday, go back to the kitchen and eat some more, if you can, before going to sleep. This was frequently just three to five spoons of peanut butter or a bowl of ice cream, but I was a dirty bulker. Over time my weight trended upward. Although now I have a real hard time falling asleep if I'm hungry, and fall asleep really easily after meals :P