As a native English speaker, I have never heard of loose skin for a human being referred to as "baggy", but I have heard "baggy skin" being used for Elephants and Rhinoceroses.
I would advise against using the term "baggy" to refer to skin, as it may be outdated.
It would sound more natural so say "wrinkled" or "wrinkly" skin for loose skin, not baggy.
Sometimes people might say they have eye bags, or under-eye bags which sounds similar. This means a hollow or puffy/swollen under eye area from lack of sleep (same area as "dark circles").
I hope that helps!