Can I use an outlet splitter with my air conditioner?
Your AC only draws 6.3amps when its running.  But when it turns on, for a moment as the motors start, it draws significantly more.  Many window air conditioners say in the manual that they need a dedicated circuit because of this.

These startup surges may melt cheap powerbars and splitters, eventually causing enough damage to be a fire hazard.

Additionally, those surges cause the voltage to drop which can wreak havoc on delicate electronics like an electric piano.  Usually not destructive, but enough to make it malfunction.

Assuming you cant get permission to have more outlets installed, run an extension cord, preferably for the other electronics near the window.  Make sure that extension runs to an outlet on another circuit, and that no other large loads or sensitive electronics are on that circuit.