Thank you. There is chapter by Mark Bracher in his book Radical Pedagogy that explains the drawbacks. Obviously, I cannot explain it in comments. I would recommend reading up on the criticism of new historicism. This is just an introductory video.
Here is a resource from Purdue U. Take a look at their references: owl.purdue.edu/owl/subject_specific_writing/writing_in_literature/literary_theory_and_schools_of_criticism/new_historicism_cultural_studies.html
Sorry, I have no opinion on it. I will ask around, but in the meanwhile please ask around and see which book professors are using for the course on History of English Language.