Answer:
The doctor explained to Silvia that she felt better and later got sick again because a few doses of the antibiotics killed most of the germs that made her throat to hurt. But some tougher germs needed more doses in order to completely kill them. So her stopping the antibiotics after few days she got better, made those tougher germs to be come alive thereby causing her more sore throat.
Below is an evidence from the text; a comment from the doctor:
"That's why you got sick again," the doctor said. "Most of the germs that were making your throat hurt were killed easily by a few doses of antibiotics. That's why you felt better after a few days. But some germs are tougher, and you need more doses of the drug to kill them. When you stopped taking the antibiotic, you left the toughest germs alive. These bacteria reproduced, and now you have many of the toughest kind causing your sore throat."