That's an unenviable position, but it's not an uncommon one! I definitely think, without knowing anything at all about your scores, that you should take advantage of the free date change and postpone til April if you're scheduled for March.
For me to tell you much else, though, requires more info about you! What was your diagnostic score, and when in your studies did you take that first exam? When you saw improvement in Feb, how much? What were you scoring? And what are you scoring now?
Now, I'm of the opinion that nobody should be shy about sharing scores, getting answers incorrect in class, etc., because the LSAT primarily measures how well you take the LSAT, not your intelligence, aptitude, or personal worth. But, if you'd rather share that with me via email than in a public forum, feel free:
ldamone@manhattanprep.com.