I'd be very grateful if anyone could help me ID this plant.

I've been given a potted "shrubby" vine, but am not sure of its true identity. The people it came from call it "jasmine", but I've looked and looked online and can't find a form of jasmine (or plants commonly called "jasmine") that look the same.

It originally came from (I think, northern) Mississippi, but also lives here in coastal Alabama (8b). I've been told that it was cold-hardy in north MS, likes full sun, and grows as a vine.

The largest leaves are just over an inch and a half long. Matte/not shiny. Medium-to-dark green with paler veins. Fairly thick leaves, for their size. Gently toothed edges. I thought the leaves were placed opposite, but looking at it again, they seem to be slightly alternate.

The vine is sturdy, but still somewhat supple.

I haven't had it long enough to know when it blooms-- but I've been told that the blooms are white and extremely fragrant.

Thank you for your time!