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.
There's a lesser form of tone-deafness (perhaps that's not the right word for it) where you can't tell with certainly or consistency the direction or extent of a change in pitch.
You can still hear and appreciate music, but you can't whistle or hum along to a tune.
I know someone who can sing to match a melody from memory very accurately. They sing on key. But they have a hard time singing to match a single pitch, and they have a very hard time naming whether two consecutive pitches are ascending or descending.
Definitely possible, but I suspect there are also quite a lot of people like me, who have a fairly poor ear for intervals (let alone absolute pitch) and are baffled by a lot of the things that seem 'obvious' to others, but wouldn't meet the criteria for amusia.
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.