Leo would probably take charge immediately. He'd be focused on getting Mikey to safety and finding a way to treat his injuries. He might be blaming himself a bit for not being there to protect Mikey better.
Raph usually gets really angry. He blames himself for not being there to protect Leo or he gets mad at the enemy who hurt Leo. He'll be the first to want revenge and will be very protective of Leo while he's injured.
Leo would likely take charge immediately. He'd assess the situation and start giving orders on how to help Mikey. He'd be calm on the outside but worried on the inside.
Splinter, as their sensei and father figure, would offer wisdom and comfort. He might have some traditional methods to help with Donnie's pain and healing. And he would also use this as a teaching moment for all of his sons about the importance of caution and looking out for each other.
In a fanfiction, Mikey might get hurt during a mission to infiltrate a Kraang base. He could be detected by security systems and get zapped by some sort of electric defense mechanism. This would leave him weak and in pain. His brothers would need to carry him out of there and find a way to reverse the effects of the zap. They'd be desperate to get Mikey back to his normal, energetic self.
Well, Leo would be the calm and collected one showing concern. He'd organize everything from Mikey's care to the security of their lair. He might also give Mikey pep talks about getting better soon. Raph would show his concern through his actions. He'd be the first to volunteer to go out and get anything Mikey needs, whether it's medicine or his favorite food. And Donnie would be constantly hovering over Mikey with his medical equipment. He'd be making sure Mikey is taking the right medicine at the right time and monitoring his progress closely. All of them would also share memories with Mikey to keep his spirits high.
Inuyasha would likely be very angry and protective. He'd probably rush to her side immediately and vow to take revenge on whoever or whatever caused her harm. His reaction would be intense, as he has deep feelings for Kagome.
Other characters' reactions can vary widely. Some of the more empathetic classmates, like Tsuyu, might offer words of comfort and stay by his side. Mineta might be a bit more cowardly, but still show some concern. The teachers, such as Aizawa, would take charge of the situation. Aizawa would ensure Midoriya gets proper medical attention and also start an investigation if the injury was due to foul play. His mother, if she were to find out, would be extremely worried and rush to be by his side as soon as possible.
One possible scenario could be that Mikey gets hurt during a fight with the Foot Clan. Maybe he underestimated an opponent and got a nasty cut on his arm. His brothers would then rush to his side, with Donnie trying to patch him up as quickly as possible while Leo and Raph stand guard, ready to fend off any further attacks.
Leo would likely take charge. He'd be calm on the outside but worried inside. He'd make sure Donnie gets proper rest and tries to organize the others to help. Raph might be a bit gruff at first, but he'd actually be really concerned. He might offer to get supplies or guard Donnie while he sleeps. Mikey would be the most emotional. He'd probably be constantly by Donnie's side, trying to tell him jokes to make him feel better.
One common way is in a fight with a powerful enemy. Maybe a new mutant or a really tough Foot Clan member. Another way could be through some sort of accident, like a trap that was set for the turtles.