Thank you for your response.
I was concerned about a fever, because that make me believe you really should see your doctor to be tested for signs of bacterial or viral infection. A simple blood test may provide an answer - your doctor can do a blood count and check for any illness that may have come about from insect bite, such as ticks or mosquitoes also.
A stiff neck can be a sign of meningeal irritation - inflammation of the lining in the spinal cord. Recently we've read too much about West Nile virus, Lyme disease and even Rocky Mountain Spotted fever. Rash can accompany viral infections and is associated with Lyme disease and other systemic illnesses. Meningitis is associated with severe headache, rash, high fever, and stiff neck. Your symptoms are mild, but they still add up.
It would be better not to write this off to an allergic reaction. . You may not have access to your doctor today, and 24 hours has passed since you submitted your question. I think it is best to visit the emergency room or walk in clinic, or even an Urgent care center rather than take a chance that this is not serious. It is always better to be cautious, especially with the symptoms you've described. Here is a link also:
Please let me know if you have any further questions.