Elsa's definitely sick – she's practically on fire. She looks surprised at the contact, but doesn't move away. It's only when Anna realises how close she's gotten that she steps back.
Brain desperately trying to catch up with her actions, she flounders for a second. Luckily, Elsa speaks before she has to think of something.
"I'm fine," she stresses, staring Anna down. It's ruined when she begins coughing, and then doesn't stop. Anna's hand rubs circles into her back, helping. When it does abate, she just says softly,
"No, you aren't."