Thank you for your query.
It is not possible to tell what type of insect bit your daughter by the description given by you. Any insect bite can be followed by a larger area of redness
around the bite.
How much has been the termperature? You have not mentioned it except saying "showing signs of fever". Several bug bites can make a toddler irritable and she is bound to be "not herself". I suggest that you wait and observe for another day or two.
I hope I have answered your query to your satisfaction. Please do feel free to update on the situation and feel free to revert back if any clarification is required.
Wishing your daughter all the best.