1. It is visible in Louisiana from about the months of November thru January.
2. It rises in the east and moves west during the night, of course. It rises (becomes visible) higher up as the months go by.
3. The “kite” part is approximately the size of a full moon.
4. The tail part is vertical and I think it hangs a bit to the right.
5. Right now it appears to be at about eight o’clock. The moon is too bright and it is hazy.
I’m in Georgia and so we are seeing about the same things, just an hour later.
Which side of the Moon?
I am now getting the feeling you are talking about maybe the Water Jug in Aquarius. More to the West would be Delphinus, the dolphin. To the east might be Ares.
Above would be Andromeda, but, that’s bigger than the Moon.
Keep it coming!
Not trying to be dense, it’s just what you are calling a kite might be something I call something else.
Everything I posted is above the horizon right now.