Sick for almost a month now???

My brother has been sick for almost a month now. At first it was just a sore throat and coughing. Mom took him to the doctor and they said it was a viral infection and prescribed some sort of Antibiotic. They said he would be fine in about a week. Well he seemed like he was getting better, then when it came time for him to go back to school, he got worse. He has his previous symptoms plus a runny nose and sneezing. My mom hasn't taken him back to do the doctor but she called and they prescribed him Amoxicillin. What the hell is going on here? What would cause him to be sick this long??

Bad luck. My child got sick several times in a row so him being sick lasted about a month.