Will push-ups make your arms bigger?

I'm tired of everyone at school thinking I'm so wimpy and skinny, and that I am just skin and bones. My legs are fine and muscular, but my arms are too skinny. Right now I am trying to do push ups to make them bigger and more muscular. Will doing push ups make my arms bigger? How long do I have to do push ups to make them bigger? Like, 3 times a week for a month or what? Are there any methods I should try? Thanks. I'm just so tired of everyone thinking I have no muscle at all.