Phantom limb is in reference to the phenomena in which amputees experience sensation in their nonexistent limbs. What you are describing (assuming you aren't literally talking about a disembodied limb) is alien limb in which a transplanted limb seems to take on a mind of its own.
Phantom pain fucking suuuucks. I've been an amputee for 10 yrs and I still get them. Think big ass kitchen knife put in a furnace then stabbing you through the shin for 10-15 seconds.
I take percocet twice a day but science has yet to pinpoint what causes phantom pain. It happens so fast that there's nothing you can do about it. It was worse the first few years, now I only get it a few times a week.
I also take gabapentin, which is a nerve blocker. It was crazy the first few years b/c I had to sit in front of a mirror and say out loud that my leg wasn't there. It helped to build new pathways in my brain and block out the old ones that thought my leg was still there lol.
Sometimes (even though I've never used my "real" leg) I can get out of bed in the morning and kinda just stand up like a normal person, and then fall on my ass as the coordinated fucker I am
https://en.wikipedia.org/wiki/Alien_hand_syndrome