Is pier a common noun

Yes, the Word pier is a common noun, a general Word for any type of pier anywhere.

A proper noun is the name of a specific person, place, or thing. A proper noun for pier is the name of a specific pier, such as:

• Pier 39 Concourse, San Francisco, CA
• Steel Pier (amusement park), Atlantic City, NJ

The verb, peer, is spelled differently, as in "I decided to peer into the fish tank to see if my angelfish was still alive." Peer can also be a noun, as in " I wanted to ask a peer if my answer was correct."