You can always tell when you're reading a manwha, and not a manga. The girl main character with long wavy hair, and huge sparkling eyes. The love interest with a pointy chin that could stab someone's heart and big sparkly eyes as well. Then of course, you can't help but notice that everyone seems to be involved with some kind of gang, or bullying - and the fanclubs.
And that's when you notice Don't Touch Me! is a parody of all those other manwha's out there that are exactly like that - but take themselves far too serious. In later chapters, it now deconstructs the tropes found in this manwha, which makes for an interesting read. So the earlier chapters are parody, and can probably make you laugh a few times, and the later chapters will try to deconstruct these parodies and give a real world spin to them.
The Manwha is about a girl named Mirang, who as a little kid, always used to bully a boy who was friends with her brother. Because he took her brother's time away from her, she hated him, and bullied him. She hit him, threw rocks at him - awful stuff. But the boy named Won would always say it didn't irritate him, it didn't bother him, it didn't hurt - and that pissed her off. Later on she moves away, and comes back 7 years later, where she sees he has grown up way taller than she has. She notes he has a weird looking face, when previously he had a cute face and she promptly starts to make fun of him again, even hitting him again. Won again says it doesn't irritate him, and Mirang faithfully noted that even though he grew up, he was still the same Won - and she liked it.
The heart of the story is about Won's face. Won apparently grew up looking hotter than the hottest guy on earth. This made people (men and women alike) fawn over him, and get into fights over who would approach him first, or date him, or touch him etc. Eventually they all decided to never touch Won, so that they could all stop fighting, and the fanclubs were born. Because everyone started to avoid him, Won begins to think his face is ugly, and decides to cover up half his face with a scarf to not make people so uncomfortable around him.
Funny thing is, Mirang will gleefully note his face makes her laugh, something she considers a great compliment because her ideal man is a comedian who makes her laugh - but to Won it's like a stab at his worst insecurity; his face is so ugly it makes her laugh. That's where most of the humour comes from.
Don't Touch Me is about Mirang liking Won and trying to get him to like her back as well, while the plot will deal with Won's pretty face and his overly obsessed fanclub with him. In later chapters this gets deconstructed and adds just the tiniest bit of realism to it.
It's a funny story, a parody really, with likable characters and charm to it. It's not to be taken serious, and it doesn't pretend to be anything different - which is why I like it. Give it a try and read the first 10 or so chapters, if you found you still don't like it, then it's not for you.