You don't need the resources from eating plenty of food if you don't put it to use. Be glad that you're skinny and not fat.
It's possible that you have a fast metabolism, but judging from the meals you miss it's more likely you're winding up with malnutrition.
My advice: Your body will fix itself and get into balance if you make it your top priority - so find a sport or hobby that makes you a lot more physically active and be consistent with it. Your goal is to make every day, a day where you exerted yourself instead of nothing at all.
I would suggest swimming, but that's a biased answer since it coming from me.
The point I'm trying to drive through is that it's a problem you CAN do something about.
I'm 17 and in the same weight group, just a bit taller, and worry about being skinny myself, especially with my grandma nagging about it all the time. But I've also heard that grandmothers are notable for that kind of thing.