What Could Be The Reason For Cough, Rash Behind Ears And Arms, Headache In A Child After Being Bitten By Mosquitoes?

My 4 year old son has a cough, he was coughing to the point of making him throw up this early afternoon. He still has a cough, his sinuses feel a bit swollen, he said his head hurts, and he was sneezing a lot. I gave him Benadryl and it seems to have slowed the sneezing enough for him to fall asleep. However now (he s sleeping) but is coughing a bit and is badly sweating, his temp is 96.9 - I just brought him to the e.r Sunday because if a rash on his left arm, behind the left ear, left side and foot. We were told he was attacked by Mosquitos and he was out of there within 5 minutes. The cough wasn t addressed at that time. Can this be from the bites or the bad flu going around? I pretty scared about it as we have a 2 yr old and a 1 yr old and their dad was just released from being in icu for pulmonary embolism. Thank you for your time Martha