I look forward to seeing you .
( I never saw "I look forward to my seeing you ", so I don't know whether it is right or not. )
Ok,I will give you two explanations.
1 ) English explanation:
Look forward to is one of the many phrasal verbs in English in which an adverbial particle ( forward ) as well as a preposition ( to ) is combined with the stem verb to signify a particular meaning. What we are looking forward to can be exemplified as either as a noun phrase or as a verb-phrase with an -ing pattern
2 ) explanation from a Chines dictionary,《 A DICTIONARY OF CURRENT IDIOMATIC ENGLISH 》
expect with hope or pleasure:
I'm looking forward to seeing you again soon.
My son is looking forward with eagerness to your visit
Student or Learner