Dean was never okay with being sick. He didn't like the helpless feeling, and he sure as hell didn't like his dad telling him to "Suck it up! Demons aren't gonna stop trying to kill you just because you have a cough!"
So when Dean was sleeping on the couch, looking like death warmed over, Sam just covered him with a blanket. "Sorry, Dean," he whispered, not really wanting to wake his brother up. "I'll go work on this case by myself. I'll be safe, I promise. Just..." Sam paused, torn about dealing with a vampire or taking care of his brother. "Just rest well, okay?" And with that, he walked outside of the motel.
"Dear Castiel," he called. "I know you prefer to answer to Dean, but this is about him. He's really sick, so if you could come down and watch after him while I'm gone... I'd really appreciate it."
Sam opened an eye for a moment. He sighed when he saw no sign of Castiel, didn't hear the tell-tale flutter of wings that marked the angel's arrival. Sam shook his head, got into the Impala, and drove off to take care of the vampire.
Sam wasn't aware – not until later, at least – that Castiel did hear his prayer. He didn't appear to Sam, but instead teleported directly to Dean's side.
When Castiel saw Dean, saw how truly sick he was, Castiel had an idea. Of course, with his powers he could just heal Dean entirely, but that wouldn't be as enjoyable as what he had in mind.
Instead, Castiel touched his hand to Dean's shoulder, just as he had when he raised him from Hell, and he took away almost all of the sickness.
"Cas?" Dean muttered as he slowly woke from his fever-induced sleep, sitting up on the couch.
"Don't worry, Dean," Castiel said calmly. "You'll be okay." Castiel sat down next to him and wrapped his arms around Dean.
Castiel leaned down and was about to kiss the hunter, but Dean jerked back. "Dude, I'm sick."
Cas withdrew, hurt drawn plainly across his face. "Dean, I'm an angel, sickness doesn't affect me."
Dean's face fell when he saw Cas's expression, and he reached his hand up to cup the angel's neck, his thumb reaching out to caress his jawline. "Just habit, I guess. Sorry."
Cas's face softened again as he leaned into the kiss, laughing softly when Dean had to break away so that he could breathe through his mouth again. Castiel laid back on the couch and pulled his hunter close, using the illness as a reason to be near him.
Dean wrapped his arms around his angel, just as Castiel did the same. Right before Dean fell into another slumber, he heard Castiel murmur, "Rest well, Dean."
As Castiel said that, Dean also heard the sound of fluttering wings as a soft, feathery warmth surrounded him.