Are you at the tail end of a regular fall semester? Are finals in about two weeks?
Are you dropping an English Literature class, or is it a full-fledged change-of-majors?
Is the English Literature class one of your required classes to graduate with the degree you want? (ie, “12 hours of English classes— pick four from this list of twelve” or something like that?)
If you’re 90% of the way through with your class, you might consider seeing it through all the way, and save yourself the expense of re-doing the credit hours, plus the impact on your future schedule of taking a replacement course, plus the impact on your GPA for canceling the class after the deadline for canceling classes. It might be a hold-your-breath-and-pinch-your-nose sort of thing, but it might be more prudent to finish seeing it through, rather than just wiping your hands of it.
However, if your English Literature course is just one example of how things are a bit too far left at your university in general-- you might also consider positioning yourself to transfer to someplace a little less extreme, and is more in line with your values.