To add another possibility, if the sound cycles on and off consistently with the AC compressor, and is not apparent otherwise, sound from that right side could be coming from the radiator fan. If the engine isn't overheating, the fan would normally be off, but it comes on with the AC compressor. There could be a broken blade, or something caught in the fan, or perhaps the fan motor itself. (That goes for both fans, which are turned on when the AC compressor is running.)
Also, there's added load on the crankshaft pulley when the compressor is operating. I wonder if both drive belts are in good condition (nothing slapping around), and if the crank pulley is running true. A recording of the sound might be useful.