Shortly after that I had a dream, I know it was a dream because I actually saw what I wanted to see in front of my eyes and it was very realistic as opposed to imagining something, for example.
And I remember being able to actually control what I'm seeing.
If you knew at that very moment that you were dreaming, then you were lucid.

How do I know if I really had a lucid dream or if I dreamt of having a lucid dream?(In that normal dream, I was telling people about the lucid dream I just had).
Sounds like you had a lucid dream, followed by a false awakening (common after lucids) in which you were sharing your experience, like you're doing now, only unaware that you were still dreaming.