An instrument is a precision, maybe scientific, device, such as a blood pressure monitor. It can also refer to a musical instrument, maybe because both are considered delicate.
A tool is something tradespeople use, such as a hammer. or screwdriver.
An appliance is usually operated by electricity and used at home: washing machine, vacuum cleaner,blender, etc. In the medical field, artificial arms or legs, or braces to make your teeth straight are also called applieances.