In your example, I would say, "We're NOT strangers."
"no stranger" is used in a different context.
She's no stranger to something = she's familiar with something, or she's had a lot of experience with something
She's no stranger to hard work (=this is something that she does all the time).
That TV show is no stranger to controversy. (=they have had their share of controversies over the years)
He's no stranger to conflict (= this is something that he deals with frequently)