Kybella to the neck?

The first treatment with Kybella tends to have the most swelling. Minor bruising is not uncommon. Neck compression garments and arnica (topically or orally) have not been shown to reduce swelling or bruising, but some patients do feel that arnica tablets, in particular, may help. Being upright and exercising may also help. Good luck. 

Kybella does not require post treatment wrapping or compression although it could not hurt if you wanted to do this.  Applying arnica can help with bruising.