Why do my sent emails show up in inbox?

I have a gmail account that I use for my iphone email. Everything works fine, except...whenever I send someone an email, a few minutes later I hear the "email chime" and I think "oh good, they just wrote back." However, sitting in my inbox is a copy of the email I just sent to the person. Any ideas why this happens and how I can get this to stop?

I went in to my email settings and "Always Bcc Myself" is OFF.

Thanks!