Can you be anerexic and not know it?

Hi, im 13 and i am really skinny. I have always been little though. I weighed 3 lbs when I was born. And I currently weigh 75pounds. Im about 4' 10'' I never skip meals and I eats snack about every 2 hours to keep me well nourished. I also hydrate myself a lot. I drink milk with a whole packet of Carnation Essentials am just really scared that I am going to die from being skinny. Because there is nothing I can do about it I eat a lot but I never gain weight. If this helps, both my dad and my mom are very slender. Please help I am freaking out I don't want to be one of those kids with those tubs that they get fed through put into their stomach. And I don't throw up after I eat I actually have a fear of throwing up. Like if I ever feel like I am about to throw up I will literaly do everything so that I don't I will get a Pepto Bismal from my parents and I will like lie down and eat peppermint stuff. Anyways, I just want to know why I am so skinny!?! Please no rude comments. I am just scared and I do not want to die. I LOVE LIFE! <3. Thanks.