The New Kingdom predated the founding of Alexandria by almost 1,000 years. Alexandria was not founded until 332 B.C., when Alexander the Great, having conquered Egypt, constructed his capital there. It was a Hellenistic city, whose culture and ruling elite were basically Greek in character. It was precisely to get away from Egyptian traditional notions of political power that Alexander built his capital there. The Alexandrian school of medicine was a Greek, or more accurately, Hellenistic institution, not an Egyptian one.
The New Kingdom, on the other hand, ended in the eleventh century B.C. By the time Alexander conquered Egypt, it had ceased to be an independent political entity for centuries. Alexander claimed Egypt from the Persians, ending a period of Persian rule that had lasted for about two centuries. In the centuries before that, Egypt had been ruled by a variety of foreign peoples, including the Nubians and the Assyrians.