病毒或细菌感染,什么时侯用抗生素?

My daughter has fever since last Saturday. On Monday I took her to see the doctor and was told it was virus infection. On Tuesday, took her to the summer skating camp, after she got home, her condition got much worse. Started to cough badly and had102F temperature. Since then, I kept her at home for the rest of the week. On Friday morning, I took her to see the doctor again (this time met different doctor in the same clinic), her temperature was measured at 100.1F. He prescribed the antibiotic medicine based on her fever lasting 7 days. I just wonder how a doctor can determine if the infection is caused by virus or bacteria. If it is a really virus infection, then antibiotic medicine is useless. He didn’t do any mucus culture. Anyway, on Friday afternoon, I gave my daughter the first dose of the antibiotics, she has no more fever in the next day. Wonder if her own body immune system made the fever gone or the medication? Usually it takes 3 – 5 days for fever gone, but this time it took her a little bit longer time to recover. By now, I am still not sure if the medication is really necessary for her case or not. Since she started the medication, now I have to let her finish all the medication (total 5 days although she felt better right after the first dose).