I think that problem could be solved by getting some high quality LED washer nozzles. I hear that green works the best.

Before I get blasted.. I am kidding.

If you hear the motor trying to push fluid, then its not a relay or fuse.

If you wax your car and get wax in the nozzles this can clog them up. Try carefully cleaning them out with a pin. You can also aim them that way.

What year is your car, I will try to get you some details as to which fuses to check if the motor is not making noise.