Is throat a common noun

Yes, throat is a common noun, a Word for any throat of any kind.

A proper noun is the name of a specific person, place, thing, or a title; for example:

• Throat River, Unorganized Kenora Region, ON, Canada
• Devil's Throat at Iguazu Falls, Argentina
• Berkshire Ear, Nose, Throat, & Audiological Associates PC, Pittsfield, MA
• "Throat", a novel by R.A. Nelson