What is the relationship between the male and female character? In the short Me Me Me, the male character seems to be mentally tormented by a female character. There are various hints in the short about the relationship of the two. Is there anything official describing the relationship between the two characters?
In the western side of the web, probably not. The only official description is

“You are attacked and ravished by many girls”

That really does not answer the question. But looking up for explanations of the symbolism, I came upon two analysis of the video: the first one by NewVagabond.tumblr, the other one on the Ask John column of animenation.net. They are lengthy and detailed, full of screenshots and worth reading. Go read them, I'll wait.
At the end, the writer behind &quot;Ask John&quot; says:

After composing my own interpretation, I did a web search for other criticisms and interpretations. I encountered a number of analysis that interpreted the video entirely oppositely to the way I did. I encountered several interpretations that suggest that the video represents the boy’s effort to stop being an otaku, that the video is a criticism of hikikomori otaku culture.

He did his homework, it seems. But one other thing on his closing thoughts caught my eye:

(...) Hideaki Anno’s influence and involvement in the production (...)

Anno-sensei is well-known for his &quot;Death of the Author&quot; philosophy, where what the author meant with his work is replaced with what the viewer felt when consuming said work. From Anno-sensei's roundtable discussion at Anime Expo '96 convention:

&quot;Animation makes sense to people in the process of their seeing it. (...) There has to be a relationship that comes into being between the person watching and what the character's saying in the animation itself.&quot;

I am inclined to assume that the production staff of Me!Me!Me! follows the same ethos. But all this about Anno's philosophical influence is totally an assumption on my part.
Since even the know your meme page (and the linked articles therein) also do not point to an official explanation (but do comment on the confusion the viewership feels when watching the video), I end my report with:

Is there anything official describing the relationship between the two characters?

No, to the best of my Google-jutsu, there is not.

Appendix

Link to the translated lyrics.

Yet another translation, with Kanji and Romaji lyrics by newvagabond.tumblr.

The official site of Japan Animator Exhibition (Japanese) also have the Kanji lyrics.

Yes, I also felt like this: