Another possibility is that it's part of a spell gone wrong. In the Harry Potter universe, magic can be unpredictable. A botched spell could have caused some physical harm to Harry, resulting in the need for bandages.
It could be that he was in a fight with some dark wizards or magical creatures. In the wizarding world, battles are common, and getting wounded is a likely outcome. So, the author of the fanfic might have him wear bandages to show that he has been through a tough encounter.
Maybe he got injured during a dangerous adventure in the fanfic. For example, he could have been hurt while exploring a new part of Hogwarts that's filled with hidden traps.
Maybe it's for protection during some dangerous magical experiments or adventures. For example, if he is exploring a new, dangerous part of the Forbidden Forest where there could be falling branches or wild magical creatures attacking from above.
Maybe it's a dare. In the wizarding world of the fanfic, there could be a bet or a dare among students that led Harry to do this. It's a way to show his bravado and willingness to take risks, even if it means wearing a dress for Draco.
Perhaps Madam Pomfrey, the school nurse at Hogwarts. Even in a fanfic, she would be the most likely person to take care of an injured student like Harry. She has the skills and the supplies to properly bandage his wounds.
It could also be related to the treatment of Harry's friends or allies. Suppose Fudge is persecuting Dumbledore or other Order of the Phoenix members. Harry, who is loyal to his friends and those fighting against the Dark Arts, would be enraged and yell at Fudge. He wouldn't stand for any harm coming to those he cares about, and Fudge's actions in this regard would surely provoke Harry's anger.
Maybe she's yelling at Ron. Their relationship in fanfictions can be quite complex. If Ron says something insensitive or does something stupid, like forgetting an important task that could put their mission in jeopardy, Hermione would surely yell at him.
One possible reason could be a difference in opinion regarding the safety of the characters. Maybe Molly is being overly protective in a way that Harry feels is hindering their fight against the dark forces, so he yells in frustration.
Well, it could be that the Queen has a special connection to the wizarding world in this fanfiction. Perhaps she has been secretly informed of Harry's bravery and selflessness all along. And as a symbol of the British monarchy, she knights him to show that the Muggle and wizarding worlds can have a positive relationship. So, she bestows this honor on Harry.
Maybe Albus has done something dangerous or disobeyed Harry's instructions. For example, if Albus got involved with some dark magic related stuff without Harry's knowledge, that would surely make Harry yell at him.
He could wear a mask to protect his loved ones. If there's a new threat in the wizarding world that targets him and those close to him, a mask would be a way to keep his identity hidden so that his enemies can't use his friends and family against him.
Well, it could be for safety. Snape was deeply involved in the fight against Voldemort. If the Death Eaters or Voldemort himself found out that Harry was Snape's son, they would use Harry as a weapon or a hostage. Also, Snape had a very difficult past with James Potter. He might have been worried about how Harry would react if he found out that his father was Snape instead of James. Snape may have thought that keeping it a secret was the best way to ensure Harry's growth and development without the burden of this complex family relationship.