Does lying down after eating makes people sick? if yes, in what way?

It could result in esophageal reflux, with irritation of the esophagus. But mostly that's an issue of comfort, not serious health problems. If you get heartburn or a sour taste in your mouth, try to avoid large meals just before bedtime and lying down after eating. If no such symptoms, this is nothing to worry about, especially at your young age.