If they wired it backwards the hot side might be joined to the "ground" which is connected to the chassis (I don't know washer and dryer terms). So you would have a hot side on the washer and a ground side on the dryer.
A safe way to check this would be to use a multimeter to check the voltage between the washer and dryer. I'm only mentioning this because its fun to speculate. I would still wait for a professional electrician to diagnose things. They can also document what they find which helps you if you need a case.
The shock might have been bad because of the amount of contact or duration. Normal 110v shocks are really small. You brush against something, it hurts, you pull away.
In this case you might put your whole hand on it and then if you touch the dryer with any part of your body you get a big shock.
For what its worth, you won't know until the electrician confirms things. The dryer could be wired backwords and Lowes could have done things 100% right with the washer. Or there could be another problem (lose wire somewhere, possibly a defect inside the washer)