NOTE - This came from a Tumblr prompt - Loki would probably be needy and clingy if he ever got sick. I imagined it with a Blackfrost slant, of course.
Fever
Despite his mighty stamina and godly physique, Loki came down with a high fever after a long hunting trip in the mountains. By the time he returned to the castle, he was babbling about dark visions and tree nymphs.
Natasha, caught in the act of cleaning her weapons, took one look at him and sent him to bed. He complained loudly, but she pushed him between the sheets, somehow got him into clean and dry pajamas, and went off to order a large cauldron of soup.
Before she could reach the kitchens, however, he called her back. "Natasha!"
She ran back to the room, fearing he was about to invoke a feverish spell or, worse, upchuck on the blankets. "What is it, Loki?" she asked.
"Come here," he demanded, holding out both arms. "I do not want you to leave me. I want you to stay."
"For heaven's sake," she sighed. "I just want to fetch you some soup – whoops! Woah!"
Already he had drawn her to his side with his magic until she was dragged across the blankets to lie beside him. There he pinned her down with both arms and one leg, pillowed his head on her shoulder, and went right to sleep.
"Crap." Natasha tried to edge away once he began to snore slightly, but somehow Loki sensed her escape attempt and held on more tightly.
Using her extreme flexibility she was able to reach the bell beside the bed and ring for a maid. An instant later the door opened. "Yes?" the girl asked.
"Sorry to disturb you, Astrid," Natasha said. "Could you please have some soup brought up?" She eyed Loki, who looked like he wouldn't move for the next twelve hours. "Bring me some books as well. And my sketchpad."