That out of the way...
Xelian wrote:It is true that my grammar is lacking, however, I think that in time, hearing enough Japanese, I'll be able to know whether or not it sounds correct. Maybe it takes longer than I think though. I just know that the way I picked up English grammar is by listening and reading a lot.
I think you can get a very good feel for grammar just through consuming a lot of native content. I know also that this isn't always enough. When we can understand the general meaning, we tend to skip over small details, and this is where targeted study is needed. For example, a member on HTLAL (who I don't think made it over here with the general exodus) had consumed a ton of German media, lived in Germany and had a German wife. He complained that he still had issues with certain parts of German grammar in spite of all this.
Secondly, children are very good at picking up patterns, and creating patterns when needed. For example the phenomenon of nativisation, whereby a pidgin becomes a creole via the children who learn it from their parents and create structure and grammar. In addition to this, we have both had years of listening to native speech with native grammar, being corrected when we make errors and being instructed, however lightly, in things which are said and things which aren't said. We'll usually have most of the attention of a dedicated and amazing patient native speaker to correct us gently when we're wrong and praise us abundantly and be amazed when we're right. We start producing our native tongue quite slowly, even though we've had, at standard, about two years of being spoken to and hearing others speak around us.
So it is possible to pick up grammar and a feel for the language just through consumption of culture, but our acquisition was neither such a walk in the park as it begins to feel after a decade and more of distance, nor is it the most expedient route for second language acquisition. (For more on this method, check out user Bakunin's log and the links he's provided. He hasn't posted here in a while, but I really like the method he's come up with. It requires hours of complete silence and listening, with one or more natives prepared or paid to make very detailed recordings, but I tried it out for a few recordings with German, and thought it was great).
To answer your question, I would say that you should target the areas you feel you struggle most with. Don't read your whole grammar again. I think your plan to look up bits of grammar as you go along is great. Look at lots of example sentences, do drills if need be, practice using just those bits of grammar and get corrections.
Also, I'm sorry that your teacher wasn't much help. Good luck I'm rooting for you!