Why are my arms so skinny?

Okay this is completely serious, so here goes, I'm 5 foot 7 and only 17. I have always been very skinny my entire life, and wanted to change this. When i was 16 i weighed only 50kg, but for the next year and a bit i have been eating more, and bulking up and now i weight around 65kg, my legs are normal size to the average size, and my body is fine, but my arms are so skinny, what the ****? its really annoying as well, because its something people notice and it makes me look like like a bit of a joke, I'm looking into getting a gym membership ion a couple of months time, but i want to start working out at home now? any advice or any other way i could get bigger arms, cause if i eat more it goes everywhere else but my arms.