you certainly CAN end a sentence with a preposition - that rule is a lot of tosh .."up with which I will not put" (as Churchill is reputed to have said to show how silly that "rule" is!)
but the point might be moer that "originate" really means starts from -so in a way the "from" seems a bit redundant or tautological to some people.
As I said - the word itself might be seen as including the meaning "from" - and I've seen it used as I suggested above - without "from" in some cases - but also I've heard it used as you say.
I don't think it is a US / UK issue . You should follow your teacher's guidance!