It's unlikely that you're tone deaf. It's quite rare. Truly tone deaf people can't really hear music, because they can't hear the relative relationships of pitches properly. It's the relative pitches, not the absolute pitches, that create the ebb and flow of music.

I've been playing music for thirty-odd years, and I couldn't name pitches by ear most of the time, certainly not without thinking about it. I often hand-tune guitars (relatively!) if I'm playing by myself, and after a few days of that, it's not unusual to be more than a half-step out of whack. I don't notice, because it's in tune with itself.