HELP! Will I grow taller?

Some background information about me is that I have a strong Mongolian lineage, and I read that the average Mongolian female is about 5' 6" (I am a girl soo... :p). Growing up in Mongolia, I know that some of the living conditions means a limited diet, because for the first 5 years of my life, I probably did not get the essential nutrients. However, I moved to America, but did not start eating right until I was about 11 or so... I was always on the lower half of my class when it came to height. I am 13 now and is about 5' 2". Just recently, I have started getting constantly hungry, and I try to make sure that I eat all healthy foods, regular meals (though I have had to snack recently every hour or so) and also exercise. Because of school, I usually ended up "undersleeping"... I started eating immensely due to my hunger about January of this year... During about February or March, my arm span was 60 or 61 inches. Now, my arm span is 63 inches... If it helps, I started my period when I was eleven... Because I have been eating right just recently and more nutritious foods last winter, I have been starting to grow at a good rate again. Compared 2 years ago, I have probably grown maybe 2.5 inches. My oldest sister is about 5' 4" (she is now 22) and my older sister is 5' 3" (she is now 16). However, they did get mostly dad's genes, and I have seen mostly mom's genes kick in for my situation. Mom said that when she was growing up, she was usually one of the taller kids in class, although I have the opposite story (my mom grew up in Mongolia but I practically lived over half my life here, if that would make a difference). My mom is probably 5' 4" and my dad is (I can only vaguely remember) 5' 9" or so, giving or taking a couple inches. My cousins from my mom's side, on the other hand, are about 5' 7" or 5'9". But my question is, would my bad malnutrition state from when I was younger could have affected my height overall and future height? Also, can better sleeping patterns over this summer help with my growth? Any information would be helpful in figuring this out! Thanks! :)