You have to use “a”. Otherwise, they are both fine. ‘Back’ adds information that it is further in the past or in a time that was different from now. The principal said “The last strike in this school district was three years ago. I was a teacher then.” (Not the principal.) “What was I doing in 1975? I was a teacher back then and I never would have guessed where my life would take me.”

Either are correct, but to me, ‘back then’ is more common in the US and sounds more informal.

1st one

I was a teacher back then.