Is aunt a proper noun or a common noun

Common noun. Although if it's like Aunt SoandSo then it's a pro-noun. But if it's just aunt, like, my aunt and I went shopping. Then it's a common noun.

It's both, depending how it is used.

It's a common noun when you say something like "Oh, that's Bob's aunt."

It's a proper noun when you say something like " Oh, that's Aunt Grace."