This story takes place during the time period that Cas was human. Specifically around Season 5 episode 18, after using the sigil to send all the angels away to rescue Adam and after defeating Pestilence. As requested by Supernatural_Ellie: a sick Cas needing care from our favorite Winchester boys.
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Cas had been barely gone a day, after defeating Pestilence, when he noticed that he couldn't stop coughing. He had tried drinking water and taking medicine, once he finally asked someone what they recommended he take, but nothing was working.
He finally gave up and called Dean the next morning, when he could barely swallow. The older Winchester had insisted that Cas get his de-feathered butt over to their motel right away. So that's where he was headed, to the motel on a bus and feeling positively miserable. He kept telling Dean he thought his vessel was broken, which only served to cause Dean to laugh at him.
He finally staggered up to Sam and Dean's motel room with a hard wheezing cough. Dean opened the door regarding Cas with a look of deep concern.
"Cas, you look awful. Come lay down." Dean said quickly, leading the former angel to lie down on own of the beds. Sam grabbed a thermometer and a glass of water for the angel.
"I'm -cough- not sure- cough- what happen -cough- ed." Cas coughed out. He took a sip of the water, and held his breath so that Sam could take his temperature.
"101.4, its a fever. Not terribly, but a fever none the less." Sam said to Dean.
Dean nodded and walked over to his bag, pulling out some meds and a togo menu. He handed the menu to Sam and the meds to Cas.
"Take the tylenol, it should lower your fever." Dean said stiffly. "Sammy, order something that sounds good." he added to his brother. Sam nodded and called the restaurant ordering some food that sounded half decent.
"Get some sleep, Cas. We'll wake you when the food is ready." Sam said firmly. He looked at Dean, before gesturing for his brother to follow him outside. He stepped outside and waited for Dean to follow him.
"What's up, Sammy?" Dean asked, looking back towards the now sleeping lump that was Cas.
"Cas, shouldn't be sick... We both got better right after he defeated Pestilence. He is human, which means he can get viruses... You think that's what it is?" Sam asked his older brother. He wasn't sure what to think now that their former angel friend was sicker than a dog out of nowhere.
"I agree, he should've gotten better. But maybe he is just overwhelmed, so his body is not strong enough to fight off any lingering symptoms leftover from fighting Pestilence." Dean offered, before going back inside to cover Cas with another blanket.
Cas shivered violently under the blankets, even with multiple blankets on him. Dean frowned slightly seeing the former angel so miserable.
"Cas? How you feeling, man?" Dean asked gently, earning a groan from the shivering lump.
"C..c..cold." Cas stammered. Dean lay down beside the former angel, encouraging the man to snuggle up with him. Cas curled up against Dean, snuggling into the warmth.
Both men fell fast asleep quickly, giving Sam the opportunity to take lots of pictures for blackmail uses later on. Cas woke up feeling much better, and left a sick Dean the next morning in Sam's care.