Is pockets a common noun

Yes, the noun pocket is a singular, common, concrete noun, a Word for any pocket of any kind.

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

• Pocket Road, Beacon, NY or Pocket Road, Sacramento, CA
• Pocket of Posies (florist), Albert City, IA
• Hot Pockets snacks
• "A Pocket Full of Rye" (a Miss Marple mystery) by Agatha Christie