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Here is a one-stop link for billing questions→Subscriptions and Billing - Official Apple Support. You can review your purchase history, check a specific purchase, manage subscriptions and request refunds. Look for the charges on your purchase history; from your description there’s a good possibility you weren’t charged for anything; the messages that you got were scams to steal your identity.
When you look at the purchase history you can instantly verify the charges, and perhaps recall why they were made. If any are in error that page also has a link to request refunds.
Also consider that your Apple ID may have been hacked (especially if you don’t have 2 factor authentication). If that’s a possibility see→If you think your Apple ID has been compromised - Apple Support