I would have read this somewhere between ten and twelve years ago, I believe, though it could go a year or two in either direction. It was contained in a single volume anthology manga where each chapter was an entirely different short story (most of those stories fantasy genre set in real world Japan, I believe) and I think each was created by a different mangaka. It was a physical copy, sold in English in America, and marketed to teens. I think the cover was sort of 'cute' and perhaps shojo-esque, perhaps involving pale blues and greens?
The story I remember best was about a teenage boy befriending another teenage boy who had horrible wounds on his body. At first he worried the boy was being beaten, but eventually he realized that the boy actually had special powers--he could transfer wounds and scars between people. Because the boy was incredibly kindhearted, he would take others' wounds and keep them for himself, leaving his body in constant pain.
One scene has the two boys at an ice cream shop, where they bump into a girl wearing a surgical mask that covers up some intense-looking facial scars. Somehow she becomes aware of his powers, and begs the boy to take her scars for just a few hours so she can go out in public without feeling ashamed. After she leaves the friend points out that she's never coming back to reclaim her scars, and the now-scarred boy simply shrugs and says, "I know." After this point, he starts wearing a surgical mask himself.
The main conflict is the boy's friend wanting to help him but not knowing how; I don't remember how it ends.
The only other story I remember from the anthology, if it helps, is one where a mute and/or cripplingly shy teen girl starts texting a boy from another city. They plan to meet up, but it turns out their texts are temporally "off"; one of them is somehow texting from a few hours in the others' future. This eventually leads to the boy using his future knowledge to save her life - and, I think, sacrifice his own in the process.
I believe this short story also had a text version published in English, though perhaps somewhere different than in the manga anthology.