Most folk tend to go higher if unwell due to the liver helping out with some energy to fight off the illness..........
And then there is ketones as well, which require insulin too......
That's also my experience, most recently the flu 2 years ago......
I would just test regularly throughout the day and top up the levels with fluid [if you cant stomach anything]..........so what you did was good......
the question is however, why you dropped............in theory your basal should hold you steady with no food.........have you tested the basal recently?