I got charged for an app I never even downloaded

See the Apple Support article(s) below. Link to contact Apple Support in the article.

Apple ID - If you see ‘itunes.com/bill‘ or an unfamiliar charge on your bank, credit card, or debit statement.

Normally, all sales are considered final, but you can ask for a refund.

If you have received a confirmation email, click the Report a problem link at the bottom.

Purchases problem.      

How long refunds from the App Store or other Apple services take.