Hi Kate, poor Lily hope she is ok soon.
Bethany has been a little bit like this in the last few days but without the sweating. I took Bethany to the walk in centre and after a thorough examination I was told it was an upper respiratory infection (viral infection), Bethany had also had a bit of a temperature but that seems to have gone now. I think Bethany's has been a combination of a cold and teething as well as her bottom gums are very bumpy on one side.
I'm guessing Lily's is combination of some sort of virus and perhaps teeth. I would maybe take her to the Docs tomorrow to get her checked and give you a piece of mind.
xx