Which is correct in this sentence: "me and my" or "my and my"?

1. "He affected my day."

2. "He affected my friend's day."

3. "He affected my day and my friend's day."

Hence - "He affected my and my friend's day."

You wouldn't think of writing - "He affected me day." - would you? :)

He affected me and my friend's day.

puts forward two things,

1. He affected you. (not your day but affected you in some other way)
2. He affected your friend's day.

Therefore, "me and my" is not a good combination for use in this context.

I know this question is both old and answered, but I would like to add something important.

Consider the following sentences:

John and Mary's car broke down.

John's and Mary's cars broke down.

Both sentences are correct, but they mean different things. In the first sentence, "John and Mary" are a unit that together own the car that broke down. In the second, "John" and "Mary" are two separate people with two separate cars.

In English, the genitive apostrophe-s ending is a lot more flexible than other endings (technically, it's what is known as a "clitic") and always appears at the end of the noun phrase. Hence,

the man in the black hat's bobcat

rather than

*"the man's in the black hat bobcat.

This does not change when discussing pronouns. The first question you should be asking yourself is

Are I and my friend sharing this day that has been affected?

If your answer is "no", then Justin is correct - he has affected your and your friend's days.

If your answer is "yes", then Justin's argument does not apply, and the proper question is

Is it "me and my friend" or "I and my friend"?

Which is completely up to you, as English has no rules about whether to use "I" or "me" in this context.