________________ As they played the game...I waited for someone to call "onigiri." But no one called. I was very little then. I had almost forgotten about that. [...] But they knew...there would never be room for an onigiri...in a fruits basket. -Tohru Honda, Fruits Basket
Watashi ga Motenai no wa Dou Kangaete mo Omaera ga Warui! Not really ugly, more like a character who is socially awkward and has a blind-spot with herself. This is one of the few mangas where the female lead can range from actually looking absolutely, jaw-droppingly awful and, at other times, unexpectedly cute. It doesn't technically fit, but you might like it anyway.
And I double-recommend Stalker and Sambong Barber Shop. Not only do these fit your description exactly, but there also pretty fun to read.