I assume that you are talking about your junior year english teacher. First question I would ask you is why isn't your teacher agreeing to write a recommendation? Not having a great relationship is not a satisfactory reason. During your career you may not have "great relationships" with those that you work with, but that doesn't mean that they won't be unbiased; the impression of the high school teachers that I have come in contact with is that they are dedicated to their profession and always convey a positive message.
Sorry to be blunt, but this is not about a relationship; teachers are asked to complete a survey of very specific questions about your character, leadership potential, time management and study habits, relationship with classmates, etc. They then include a short essay to reinforce the survey questions (providing examples and such).
IMHO, you definitely need to make contact with your BGO ASAP. They will counsel you as to your options. The Academy requests recommendations from your junior year teachers; in very extenuating circumstances allowances are made for your senior year teacher to complete the task. These changes must go through the proper chain of command.