You should head down to your local commercial gym, ask to speak with one of the personal trainers, hand the guy $20 and have him diagnose precisely where you are weak. Tell him that you have X number of weeks to do Y number of pull-ups. He or she will get you there.
I was skeptical about a personal trainer at first, but found that a personal trainer working with my DS made all the difference in the world. My DS had been practicing for months and saw little improvement before he asked me to put him in touch with a personal trainer. For my DS, the trainer immediately identified that my DS needed to work on his lower back muscles to improve pull-ups. It seemed counter-intuitive to me, but it worked!
You should do this TODAY. I don't think you have enough time before February 28 to try to figure this out on your own at this point.