If the battery light comes on, it points to the alternator, yes. It sounds like the car has also gone into "limp mode". Is the engine management light on?
Though, the fact that you say you washed the engine bay means that it could basically be anywhere in the electrics that you've created an issue, especially if you did not carefully cover all electrics before washing.
It's too late now, but here is sage advice: Never wash the engine bay by spraying water. Never. On any car. Use a damp cloth at most.