Re: Metallic Chemical like taste.
First, look down the stem with a light and see if there is any corrosion/rust, exposed metal from chipped plating.
Second, if you have a non-washable hose it could be rusting. You can gut it and home depo it with some rubber tubing and hose clamps.
Third, It could be what you wash it with, any cleaners, solvents, or soaps?