Author note: I'm going to try to make this story as canon as possible. Meaning Donatello is not a doctor, and Michelangelo can not cook. If you need proof of that canon, I'm more than happy to provide it. :)
During the Battle Nexus, when watching over Leonardo after he'd been struck with a poison dart, Donatello says, "What can I do? I'm an engineer, not a doctor." So by this, it's safe to say that Donnie doesn't know medical science. And if he does, it's probably limited to bandaging minor cuts, or putting cold/warm clothes on an ill person's head.
During season 1, while Leonardo is out fighting for his life against the Foot Clan's ambush, Michelangelo is cooking breakfast. But he ruins the sunny side up eggs, burns the toast, and when April asks what's burning, Raphael replies, "Mikey's cooking," as though it were normal for Mikey to mess up his cooking. That leads me to believe that it's not Mikey who's the "Master Chef" of the household. My personal head canon theory is that Splinter is the head chef. I mean, he did raise the boys. And considering, unlike the 2012 TMNT- where they didn't know what any other food was besides algae and worms, the 2003 turtles are fully aware of different types of food. And even if Splinter didn't cook food for them, in the Origins episode, Splinter is shown feeding the turtles pizza before the group is even fully mutated. They probably lived off food that Splinter found and prepared for them. Anyway, back to the episode where Mikey was cooking. You could argue that Mikey is a good chef because Raphael later says, "Say what you will about Mikey, but the guy knows how to scramble an egg." Just knowing how to cook one thing doesn't make someone a good, or even a decent chef. And that was portrayed heavily as Mikey messed up the eggs and burned the toast.
Anyway! These are just what I noticed and consider canon! If you like to believe something else, or you go with a head canon, that's totally fine. xD This is just what I prefer.

Leonardo and Raphael have never had the most peaceful relationship. They argue almost constantly, and there's never a day where pride isn't on the line. But despite that, they have an inseparable brotherly bond. One that can be expressed without the use of words, but rather sly grins, smug chuckles, and joking insults.
The boys have always been like this. Since before they could even argue with words, they would throw fits and scream at each other over small matters, then 5 minutes later be found playing together as though nothing happened.
Which was why, when Donatello, Michelangelo, and Master Splinter heard the red and blue clad brothers arguing this morning, they gave no thought to it. It would end the same, then blow over in about an hour.

"You're so frustrating, Leo! Why can't you ever just sit down and stay out of my business?!"
"Because your business is my business when it affects the team!"
"This ain't even about the team! This is just what I wanna do!"
"Well what you wanna do is going to put us all in danger!"

Raphael took a step forward and pointed at Leonardo, his finger touching his brother's plastron, shaking with anger. "I ain't involving none of you!"
Leonardo didn't bother to swat Raphael's hand away, knowing full well from past experiences that Raphael would end up just raising his hand once more and pointing at Leonardo again. "What? You just expect us to sit by and do nothing while you put yourself in danger out there?! This isn't some patrol you're trying to plan! It's a suicide mission!"
Raphael jabbed his finger a little harder into Leonardo's chest, glaring daggers into his older brother's eyes, "It's not a suicide mission! Casey and I will just be taking out all that extra Purple Dragon trash! There's too many of them to just sit and wait to see them do something on a patrol! We don't even patrol for that long! What about the scumbags that are doin' stuff when we ain't around to stop 'em?!"

It was in this moment that the room became tenser. But it wasn't the argument that caused it... It was the scream that came after it.

"LEO!"
Raphael shouted in fear, all anger vanishing before he could even get the first letter out of his mouth.
The remaining family all turned their attention to the brothers within an instant.
They were met with the sight of Raphael holding up Leonardo's limp, unconscious body.

Seconds later, the purple and orange clad turtles, along with their father, had come to Raphael's aid in slowly lowering Leonardo to the floor. Raphael was breathing heavily, panic seeping into his system rapidly, "I don't know what happened! One second I saw him opening his mouth to talk, and then his eyes rolled back into his head and he collapsed!"
Master Splinter gently tapped his son's face, hoping for some kind of reaction. None came. Worry was beginning to engrave itself deeper into the family. Leonardo's face looked relaxed, without a care in the world. He looked asleep. Peaceful. And the more peaceful he looked, the less peaceful the family felt.
Michelangelo slowly leaned closer, getting a good, hard look at his big brother's unconscious face. "Is he-...?" He cut himself off, not wanting to finish the sentence. Luckily, Donatello knew exactly what he meant, and managed to provide an answer that eased his baby brother's worry at least a little. "No, Mikey." He pointed to Leonardo's chest, hinting to the rising and falling of the plastron as the passed out turtle inhaled and exhaled. "He's breathing."
Michelangelo's shoulders dropped in relief, but soon raised again as another question settled over the room.
Raphael spoke it, "What's wrong with him? Why'd he pass out?"
Splinter, having just checked Leonardo's pulse, slowly and gently lowered the turtle's arm to the ground. He shook his head in worry, "I do not know. Your brother's heart beat is very fast and unsettling."
A moment of silence passed through the room...
Then Donatello stood up, "I'll call April. Maybe she'll have an idea of what's going on or what to do." With that, Donatello paced a little away and dialed his human friend's number.

In the meantime, Splinter asked his other two sons to help move Leonardo to the couch. Which they did, carefully. There was quiet chatter among the turtles, joined by Donatello after his call, about what could have happened.

"Maybe he was dehydrated?" Michelangelo asked, hoping all their issues could be solved with just a glass of water.
"Out of all of us, Leo drinks the most. He'd be more likely to have too much water in him." Donatello concluded without hesitation.
"Then maybe that's it?" suggested Michelangelo, "Maybe he did drink too much water?"
Raphael scoffed, then grew quiet and more serious. "...I think it was something worse."
His brothers looked at him critically, a mixture of daring and pleading him to continue his thought. Even Splinter stared at his red masked son with a quizzical eye. So Raphael spoke on, "Just... the way he looked at me before he passed out. It was like he had no idea somethin' was wrong until it hit him, and suddenly... boom... he was out just like that. I don't think dehydration or over-hydration hits you so suddenly."
Michelangelo turned his attention back to his oldest brother's limp body and his peaceful face. "He doesn't look like he's in pain right now..."
Splinter placed a hand on Raphael's shoulder, as if to reassure him. "Mrs. O'Neil will be arriving shortly. Perhaps she has the answers to our questions."
Donatello touched Leoanrdo's cheek and frowned. "...I hope so."