My Son Has Been Very Ill, Vomitting, High Fever, Severe

My son has been very ill, vomitting, high fever, severe headache, sore throat,he was diagnosed with strep throat on oCT 25TH, he finished antibiotics (amoxicillin), symptoms improved, 2 days later same symptoms came back, took him back to emerg, they felt first antibiotics did not work, started Keflex, 7 days into Keflex, he had high fever, non stop vomitting, and head ache, took him back to emerg. They took him off of antibiotic and felt he had a stomach bug. They gave him something to stop vomitting and told me to continue with fluids, that was 5 days ago. He is still very nauseous, says his throat still hurts, headache and no appetite, very lethargic. At every appointment I have asked for them to do bloodwork, every time doctor felt it was unnecessary. I am worried that the doctors are missing some underlying condition. My child has never been this sick before. First time he has ever been on antibiotic as well.
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