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)

If you haven’t already, you should probably be taking to a lawyer. Somebody fucked up and almost killed you. They have insurance for that.

"Electrocuted" specifically involves death, so in extreme, annoying pedantry, if you lived to tell the tale, technically you were only shocked and not electrocuted

Damn I'm surprised your hand is fucked, that really sucks! I've taken both 120V and 240V across the hand but was lucky with no serious injuries. Electricity is a dice roll.

Start taking pictures of all the damages before it heals and get a lawyer.

Weird timing but see this post Games that I can play with one hand

That’s shocking.

Glad you're ok and glad you're lawyering up. I can't give you practical advice but I can say there are plenty of games out there suitable for one hand and even just one button. Vampire Survivors got me through some difficult days when I couldn't spare a hand! Find yourself a distraction until you get better, and hopefully very very rich.