How can I speed the healing of chemosis? Antihistamine drops? Taping shut?

Chemosis can take a while to resolve, so be patient - it will go away!  In the meantime  you want to keep the eye as moist as possible.  When it dries out the chemosis can get worse.  So lots of artificial tears during the day, and ointment at night.  You may also want to try patching the eye at night, as some pressure may help the fluid leave the eye.  If it persists for a few weeks, it is sometimes necessary to drain the fluid - see an oculoplastic surgeon if the chemosis doesn't improve.   

Treatment for chemosis depends on different factors including the reason for the chemosis, how long it has been present, and the severity of the chemosis. The range of treatment includes lubricating drops to steroid drops/ointment to eye patching to eyelid suturing to surgery. See the link on my website for more information.

The humidifier is not too effective.  The tobradex is an antibiotic/steroid drop or ointment.  Unfortunately the product is irritating to the eye surfaces.  The dexamethasone in the tobradex does counteract this irritation somewhat but not completely.  Chemosis is swelling of the conjunctiva.  Dryness does make the situation worse.  For this reason lubrication of the eye surface with bland ophthalmic ointment at night and plain artificial tears during the day is helpful.  I would recommend that you surgeon refer you to an oculoplastic surgeon for management input.