I started in middle school around 1995 when I saw a neighbor display a message on his computer with a batch file. After that I started writing my own batch files, and eventually bought a copy of Visual C++ 1.0 (they used to sell that sort of stuff in stores) and learned C++. High school was all about learning C++ and writing various incomplete games. Then in college I majored in CS, and along the way branched into other languages like C# and Python. I also interned at a major software company, and after graduating, I went to work for them full time. Nearly 8 years later I'm still there, and am now a Senior Software Developer working on a secret project that will have an enormous impact in certain industries.
It's kind of sad, but throughout all this time I've completed a single game: a Tetris clone that I wrote in a few days back in college, just to be able to say that I've finished a game. I've worked on a variety of other things in my spare time, however, most recently a backup program that I now use to back up all my data with deduplication and redundancy.
Would you say that it's common to feel frustrated with the fact there is not time to learn everything you want to or does that not plague you?
It doesn't bother me. I think it's because I never really understood just how big the software development world was until I was fairly established as a developer.
Don't get frustrated. Just take things slowly and one day you'll wake up realizing that you know a ton of stuff. The key is to enjoy learning, and to constantly learn.