'My' is a possessive adjective telling us about a noun. The first person pronoun is 'I' or 'me' depending on its grammatical role or function. The subject pronoun is 'I' and 'me' is the direct object or indirect object.
'Pronoun' means 'stands in place' of a noun.
'This' is often used as a demonstrative adjective but here it replaces a noun, previously referred to, but we don't know what exactly.
It could be 'The (problem)'> It/This. We don't usually think of 'this' being used as a pronoun.
Words can be described differently depending on their function. 'It' would be the expected pronoun.
Where does this sentence come from please? If it is a stand-alone sentence without context it is strange. Perhaps it's a trick exercise question.