Which one is correct I am proud of my girls or I am proud of my girl's?

Thank you, thank you for asking about this pet peeve. "I am proud of my girls" is correct. You make most ordinary nouns plural by simply adding the letter s. Apostrophe s after a noun is a possessive form. For example, you would say "I am proud of my girl's athletic achievements". You are talking about the achievements that 'belong to' your girl.