Is sister's a common noun

Yes, the Word sister's is a common, possessive noun.

The noun sister is a common noun, a Word for any sister of anyone, anywhere.

By adding the apostrophe s ('s) to the end of the noun, it becomes a possessive noun, a Word that shows something in the sentence belongs to that noun. Examples:

My sister is a lawyer.

My sister's office is next to the courthouse.

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

• Sisters of St Francis, Rosebud, MT
• Sister Bay, WI (pop. 886)
• Middle Sister Wines, Napa, CA
• "Sister Act", 1992 movie with Whoopi Goldberg