Your mechanic is correct. The crankshaft pulley, key and crankshaft needs replacement by the looks of it.
Not sure what he meant by machining something though. Did he also check the timing belt, camshaft and valves as well? All ok? I hope nothing is seriously broken. Did he open the engine or just visual checking?
By the way, without the pulley, your alternator, compressor and power steering will not work because there's nothing to turn them. You have to tow your car to the shop. I'm sure the check engine light is also on. Don't attempt starting your car. You might damage something further.
As for the shop, very sorry, can't help you there as I'm located in Makati.