My son is now 3 years old and often catches colds. His last cold lasted over a month, accompanied by a few days of fever. He received several days of anti-inflammatory injections and took antibiotics for about two weeks, resulting in a weakened constitution. A pediatrician suggested injecting sedative to boost his immunity. Can he receive the injection?

Explore the possible causes of elevated platelet and white blood cell counts in children, and provide corresponding health recommendations.