Is Drain Auger good for snaking out plastic?

I have got plastic cap ( plastic nozzle of bleach bottle, not the upper cap but the one from where the liquid comes out, white one) has got stuck in the drain pipe of my sink. I opened the P trap and was trying to put bleach straight into the drain pipe by pressing the bottle and suddenly the white nozzle plastic thing went inside the pipe and has clogged the sink. The water doesnt go thorugh the pipe now as its been clogged by the plastic cap. The worrying bit is that it has gone down further the pipe as i was trying to take it out with hanger. People have suggested me to use dry/wet VAC or try auger to snake it out. Will Drain auger will get hold of the plastic and pull it out or not? Please suggest me something as i did my toothbrush in bath tub this morning .. i need my sink back to normal and i cant pay 100's of quids to plumber in this time of credit crunch too...