I mean, I think it's plenty okay to claim "professor" if you're teaching college classes. Doctor implies a certain level of schooling, but I think professor is totally appropriate, regardless of tenure or anything like that.

More importantly, there's a definite weirdness to teaching people who aren't *that* much younger than you are ((I feel much more comfortable with first graders, in some ways, than with high schoolers)) and finding whatever formality lines feel good to you is a good idea.

~Sor