Crooked Smile 8 Days After Juvederm in Nasolabial Folds, Why Would this Happen?

This does not sound like an issue with Juvederm but I would be concerned that you have developed Bell's Palsy. I would get over to a neurologist for further evaluation. 

It is extremely unlikely that your asymmetrical smile and drooping cheek are secondary to the Juvederm injections. I suggest you talk to you physician and consider a consultation with an ENT specialist to rule out the possibility of a Bell's Palsy, which is a temporary weakness of the facial nerve. If this diagnosis is made, early treatment may accelerate recovery.

 This is a bit odd.  There is a local anesthetic in the Juvederm that could affect the infra-orbital nerve however, this is a sensory nerve and not a motor nerve.  Affecting this nerve would create numbness not muscle weakness and a droopy upper lip.  If this muscle weakness does not improve in a day or so, yopu may ask the MD that did the Juvederm injections for a referral to a neurologist to rule out a Bells Palsy.  The upper lip has multiple small nerve branches, of the facial nerve, that should not be affted by injections in the nasolabial folds.