The central AC in our apartment is not working effectively in the summer; we are running the AC continuously for 14 hours a day to keep the temperature below 80 degrees. As you can imagine, our electric bill has become a huge problem. 

(**Edit:** Please note the maintenance staff are incompetent and management doesn't care about our problem **at all** -"getting the central AC fixed" is not an option, if it's even fixable)

I bought a used portable AC unit (around 11,000 BTU, rated at 12 amps) and plugged it into an arbitrary outlet near a window, because I was always able to do so with a similar AC at my parent's house. The portable unit worked great for a couple of minutes and then tripped the circuit breaker, which also shut off my computer.

After a lot of testing I have determined that all of the outlets in the two bedrooms and in the living room run off a single 15-amp circuit (which was 'helpfully' labeled "lighting" in the circuit box). This rules out every outlet that is within reach of a window. There are two circuits labeled "plugs" in the circuit breaker, but AFAICT they aren't connected to anything (unless they're for the outlets in the kitchen).

Obviously because it's an apartment I can't do anything with the wiring, and I can't use an extension cord on an 11,000 BTU AC... Am I screwed here? Is this typical for an apartment with central AC?

The full set of circuits is (as they are labeled):

* Central AC: 2x30A
* Central Heat: 2x30A
* Bathrooms: 2x15A
* Plugs: 2x20A
* Lights: 1x15A (again, this actually covers outlet in 3 rooms, there is no overhead lighting)
* Garbage Disposal: 15A (nowhere near a window)
* Dishwasher: 15A (nowhere near a window)
* Electic Range: 2 x 40A (oven/stove)