Eating is a good sign. Chickens won't always drink when prompted or watched...you can put water in a familiar container right in front of them and some will refuse because the situation is strange. However, unless she starts to have really dry poop (sign of dehydration) then I would assume she is drinking if she's also eating readily.Right now she proved that she can eat, however she didn't want to drink water, there is no discharge, her eye and nose looks clean to me, however I think she has fever and her crop is being affected, could an impacted crop cause this symptoms?
Impacted crop does not cause facial swelling, but if there is swelling more broadly of the throat area, the causation could go the other way and could potentially affect the crop. It doesn't sound like a crop issue speficially to me, but the best way to check that the crop is functioning properly is to check the bird right after roost time at night to ensure the crop is full, then check first thing in the morning to ensure it has emtied before giving access to food.
My hen that had the snake bite got hot around her face and throat, and she did sound a bit funny for a while (I didn't look in her mouth unfortunately).