Is I a common noun

No, the Word "I" is a pronoun, not a noun.

The pronoun "I" is personal pronoun, a Word that takes the place of a specific person or thing.

The pronoun "I" is the first person, singular, subjective personal pronoun; a Word that takes the place of a noun (name) for the person speaking as the subject of a sentence or a clause.

Example use:
My name is Mary. I live in Texas and I like to go swimming.

We use the pronoun because to keep using the name becomes clumsy, instead of:
My name is Mary. Mary lives in Texas and Mary likes to go swimming.

Not so smooth.