I was in a similar situation until this past March. Apartments are a difficult situation for prepping. I'm renting a house (with a 2 year contract) now, so I have a basement, garage, lots of storage space, lots of privacy etc. Ideally, getting out of that apartment would be best, but having lived in an apartment for a few years, I can understand very well if you aren't in a position to move yet.

The bottom line: Do the best you can to prepare yourself (mentally, physically, spiritually, whatever), and if that time ever comes, make the best out of what you have.