being trans doesn't require that you are unhappy with your gender, people transition based on what is called "gender euphoria" alone; "trans" just means you are not strictly / only the sex you were assigned at birth, so being gender non-conforming is already technically trans (at least when it's used as an umbrella term like this).
Gender exploration is normal in cis populations, esp. for children, but continued gender exploration and non-conforming behavior into adulthood is a common sign of being trans. I found the Transition Channel helpful for some of the basics, as well as the Gender Dysphoria Bible. Other people have told me they found the You and Your Gender Identity guide useful (here's a link to a PDF).
As far as labels, I think "gender non-conforming" is pretty broad and might work here, same for "genderqueer"; sometimes people will identify as "gender questioning" if they aren't comfortable identifying as non-conforming. You don't have to have a label, though!