First of all my first language is not English so I'm sorry if some parts don't make sense. Also i hope that i can get advice from here.

I'm a 16 year old girl, I am 5'5 and weight about 110 pounds. I have read that that weight is not really good for my age but I have a lot of fat around my thighs,my butt and my stomach. So I don't really understand. When I was little i used to be very skinny and I didn't eat healthy (my day contained chips and chocolate and sometimes normal healthy food, i just couldn't eat that normal food) but i was super skinny and my friends used to tell me "you need to eat you are too skinny". When i was 13,(i think about 5'2) i weighted only 79 pounds (in February). I started eating much more and in June I weighed about 95 pounds, my mom told me it was a little fast weight gain and i got to say I gained that weight by eating much more of those chips and chocolate, not eating healthy. In the summer it all changed, I literally ate pizza everyday until school started. In September I weighed 102 pounds. And then i started eating more normal food and less junk food. I have gained these 8 pounds in these 2 years ( I think that's normal) but I don't understand that if the weight i have is underweight for my age and height then why do i have jiggly fat around my thighs, butt and stomach that make me look fat( my arms and wrists are pretty slim actually).

 I should also say that for 10 months i have been trying to lose this fat by eating less and working out more but i have not seen any results (well my stomach is a tiny bit slimmer and I'm also better at sports than i was before). Two months ago i had this awful idea to starve myself and i looked a little slimmer after one week but then i got dizziness and felt sick to my stomach. I told my parents and they reacted quickly and made sure i ate well every day after that.  It took me 2 weeks to recover from that! A couple of days ago i thought about how badly i have treated my body and decided to start eating healthy and working out. I googled and calculated how many calories should i eat per day and i got about 1350 calories per day, i prepared healthy meals with the help of my family and felt much better and healthier but yesterday i started feeling a little light headed and today i over ate because i was super hungry. So is that not enough calories for me?

Sorry if this is long but i need advice. Am i underweight? How many calories should i eat a day? How can i lose that jiggly fat?