Yes! Congrats and welcome to the exclusive WOMENS' CLUB! It is an awesome club full of friends and supporters. When I got my first period I didn't get my next one for 3 months and thought maybe I had dreamed the whole thing. Many girls' periods are irregular and unpredictable for the first couple of years. Unless you are going more than 3 or 4 months without your period, this isn't anything to worry about (unless you are having sex or something close to it).
It most likely was your period and not having it again for 2 months is probably nothing more than a sign that your body is still working out its own rhythm. My own period was sporadic for the first year and my daughter's has taken nearly 2 years to establish a real rhythm. It's great that you are paying attention to your body and its cycles! If a more than 3 months go by and your period doesn't reappear you should tell your mom and/or your doctor.
Yes, there are a handful of things that can affect a girl's period, especially when she's within her first year or so of having them! Mine certainly wasn't "regular" when I first started either. Both my sister and I would often seesaw between longer and shorter breaks between periods until about a year into it when things started to even out. Every girl's period is different, but talk to your mom or a healthcare professional if you're worried about the irregularity of your first periods.