Pronouns stand in for nouns. Examples include:
* I
* You
* He
* She
* It
* We
* They
Possessive adjectives show ownership or possession. Examples include:
* My
* Your
* His
* Her
* Its
* Our
* Their
So, while "my" can indicate possession, it does not replace a noun.
For example:
* Incorrect: My is going to the store.
* Correct: I am going to the store.