Does this sound correct?

Strictly taken, it's incorrect.

~지만 is a conjugation with the conjunction "하지만" embedded.

And as you might already know we have "그러나" and "하지만" for "but".

그러나 vs 하지만:

그러나: "but" followed by a different point of view.

하지만: "but" followed by a contradicting aspect.

And being an American and living in Sweden aren't exactly contradictory.

Therefore, 그러나 would be the right conjunction in this case, but the ~나 conjugation doesn't sound quite natural either. (It's too hard)

~데 conjugation is the "most soft" and thus, the most appropriate "but" in this cas.

"전 미국인인데 스웨덴에 살아요"

Does this sound correct?

전 미국인이지만 스웨덴에 살아요.

Good!