Why am i gaining so much weight even though i work out?

Freshman year of highschool i was very skinny 5'0 and 100 pounds but i ate so much. Every one told me that one day i would start gaining weight because of how much i ate. Well sophomore year i was still skinny, still had a fast metabolism and i think i was like 105-110. Junior year came and i was around 115, i mean thats still decent because my body was probably still growing. In the beginning of my senior year (august) i was 117 and still 5'0. I just checked my weight again last month (december) and i was 120. I started getting really upset because i've gained so much weight so i signed up for the gym. Its been one month now and every time i weigh myself i gain like 2 pounds. I'm 130 now. Is that even possible?! How the heck did i gain so much weight. Ever since i signed up for the gym a month ago i started changing the way i eat and i started counting my calories too. I no longer eat over 1200 calories and i just have a pig out day once every 7-10 days. I usually run on the treadmill for 15-20 minutes then i do a 30 minute workout routine on my iphone app. I really don't understand how i gained so much weight! I really want to be 115 again. Is there any diet or anything i can do to make that possible? I'm so upset with myself. Everyone in my family even told me i got fatter because i have a skinny family. My family eats whatever they want so when i eat with them i always try to eat smaller portions and everything but i still don't understand how i gained so much weight so fast. Is there any possible diet or anything i can do to lose this weight as soon as possible. It makes me feel so bad i want to starve myself but i know in the long run thats gonna make me gain more weight. I'm like the fattest one in my family now. I want to be 115 before i go to college. What's the quickest way to lose weight?

You're gaining weight because you're gaining muscle from working out! Muscle weighs more than fat. If you want to just loose weight, you have to do cardio, run for like 3-5 miles a day, and keep upping it until like, 8 miles. You'll burn so many calories!

What did you do to gain weight? I've been skinny almost my whole life I'm 5, 5 and 110Lb. Would be much appreciated if you share you ideas.