The comments so far are right - use an extension cord that is rated for the AC unit. This notice from the UL is full of sensible advice, including getting an AC specific extension cord.
However, before you do that, you should do something crazy. No, bear with me. Plug a lamp into the outlet closest to the outlet you'd *like* to use with the AC unit. Then turn on *everything* in your apartment that won't suffer when power cuts out. Then go to your breaker box and flip each breaker off and check the lamp you plugged in. If the lamp is turn, turn the breaker back on and go to the next. When the lamp is off, find every appliance that is also off. All the outlets that are now dead are sharing power with the AC outlet. Unplug everything from dead outlets and flip the breaker back on. Then try the AC in the AC outlet. Bet it works.
DO NOT plug things in until the AC stops or the breaker flips on its own. An AC unit should pretty much be on its own circuit.