My pregnant wife's hand is throbbing and experiencing a burning sensation, i suspect carpal tunnel syndrome, are there any recommendations of home remedies?

Very common: Not unique to experience carpal tunnel during pregnancy secondary to focal tendinitis, which usually fades after labor and delivery. An OTC wrist extension splint could be located at a drugstore, and wearing it could relieve some of the burning.

Common hand problem: Carpal tunnel syndrome is common during pregnancy & can sometimes be relieved with the simple use of a wrist brace. These can be purchased over the counter. Frequent positional changes for the hand & avoiding prolonged wrist flexion or extension (the function of the brace) can also help. If it persists, I wouldn't hesitate to have her seen by a hand surgeon that can offer more specialized care