can I run my own unofficial contest for everyone?
Yes.
But it depends on the contest on which board you can run it: usually it's
Games and rounds, Meta is a rare exception.
And here's an example of contest/nomination which happened on Meta board,
BitcoinTalk Newbie of the Year 2021[Voting]. There's little attention though since OP didn't have enough experience.
My idea for the contest didn’t work out well, the nominees @n0nce, @kingsden, @nulluma,@myn0nce, @EZ0010 and myself sati princess have grown since then. Some of these users were also nominated for discovery of the year award. The bitcointalk community awards by icopress is much better and has more categories, amazing prizes that makes it more interesting. It’s well organized imho and has already be successful done before. The bitcointalk community awards is kinda of a big deal, it was the topic of the first episode of the bitcoin talk YouTube show.