Merriam-webster appears to disagree with you.
"America" is according to it one of three things:
either continent (North America or South America) of the western hemisphere
or the Americas, the lands of the western hemisphere including North, Central, and South America and the West Indies
United States of America
And that is already the American centric definition of the English word. So yes, "America" in English can mean both, the Americas but also either Southern America or Northern America separately, as a continent. Mind you what definition is listed first. So why shouldn't you say then that Peru is in America than?
