I don't know how up to date this site is but go here:
JLPT Level 3 Study Page
Then look up the grammar in the list in either books (That is assuming you have grammar dictionaries or textbooks) or on other websites.
A couple of websites you might want to try looking up grammar on are:
Grammar Guide | Tae Kim's Guide to Learning Japanese
JGram - The Japanese Grammar database
As far as I know the stuff on this site is user created, so be careful to read the comments on the grammar entries, just in case there are any mistakes in the examples etc.
There is also a JLPT level menu in the left hand side, but once again I think these levels are chosen by users so how accurate they are I don't know.
Japanese Verbs - Introduction and Table of Contents
Great site but it's downfall is that it's all in romaji
If you want more examples of vocab or grammar a good place to go is alc:
http://www.alc.co.jp/
Type an English or Japanese phrase or word into the search bar and hit the 英和・和英 button.
I have never taken a JLPT and if I ever do I will just aim straight for JLPT 1.
But, in my opinion the JLPT 3 stuff doesn't look complex or anything really, and from what I hear the JLPT doesn't test you on output, so having a lot of the grammar and vocab in your passive vocab I think would be ok.
Personally I think it's completely possible for you to learn all of that grammar in your time frame... Not to a point where you can use it all properly obviously, but at least to a point where you can mostly understand it when you see it.
If you haven't seen it yet look into Anki here:
Anki - friendly, intelligent flashcards
And create flashcard for things you want to remember.
Although I'm not sure how effective that will be over only 15 days.