I'd like something in which the main female lead is a lonely girl, better if a little bit ugly or fat, not so good at work and in relationships. Please, tell me that this kind of drama exists. Thank you!

Me too, flower!
Nodame cantabile
personal taste
high school king of savvy
Flower Boy Next Door
Autumn's Concerto
Kimi wa Petto

I also second Me Too, Flower! it was so good!
oh my Venus !!  (here she was ugly and fat)
she was pretty !!  (here she was so ugly and nearly ignored by everyone)
dream high 2 !!  (here she wasn't ugly but she was hated)
Heart to Heart - She's severe case of anthropophobia(fear of people). Really good!
Flower Boy Next Door