"I love myself more" is correct. You would only say "I do love myself more" if the question is "Do you love yourself more?"

Good question! And what is better to use 'I' or 'me' when I mention someone else? 'I and my friend' vs. 'Me and my friend'

According to the rules, the sentence starts with "I," so you should use "myself." Sometimes you will hear people say, "I'm going to buy ME a new sweater." The rules call for "myself."

It depends where it is being used. Using me in this way could be acceptable if considered slang or talking to a friend. Comedians also use words in this way to create jokes. But formally it would not be accepted use.

"I do love myself more." - strange "I love myself more." - good I do love me more. - strange Not clear that this is correct at all. I love me more. - Not clear that this is correct at all.