To me, single is just not involved with another person. You could be looking, not looking, etc, just not currently in a relationship.
I found my partner when I wasn't looking. I wasn't even interested in dating, neither was he, actually. We were both very, very happy single people. So yes, sometimes you find the one when you aren't looking, but sometimes you find them when you are looking - so just do what feels right to you. It does take time to heal after a breakup, so go ahead and spend some quality time on yourself right now, and enjoy being single. It can be a lot of fun!