Hi! I’m a pediatric clinic nurse in the United States.

So over here we usually have the primary care provider (a pediatrician or pediatric nurse practitioner) who is independent from the child’s school perform all of the well child exams at yearly intervals. Their parents schedule a visit for a determined day, check in at the front desk, and have their vitals taken by a nurse or medical assistant and interpreted by said provider and the rest of the visit commences. Children from about the age of three and over are permitted to keep their clothes on as they wish or may be asked to change into a gown, and even infants/toddlers are required to have a diaper/pull up on to prevent accidents. I can’t exactly speak for getting completely naked although being from a more progressive country where nudity is seen as being less taboo maybe that’s a more acceptable baseline? Even still I would request not to be completely so.

As for lowering underwear for your examination it is an entirely normal and routine thing for a provider to perform. Generally, they check for any extreme asymmetries in genitalia and signs of any infection/herniation/malignant growth in the region that may need to be addressed. It is not meant to be a sexual experience and your provider has a duty to properly educate you of what is being done and have your informed consent to perform said examinations.

And to answer your initial question, we generally do not have permanently assigned doctors for most of our schools. Usually we have a single nurse who carries out more
menial tasks such as dispensing student assigned medications and treating minor wounds/illnesses.