My IPhone has my card details stored somewhere?

It is probably stored in Keychain on iCloud --> Get help with iCloud Keychain - Apple Support

If iCloud Keychain is on, but Safari won't save or autofill account or credit card information

If Safari doesn't autofill your account names, passwords, or credit cards, or doesn't ask to save them to begin with, check the AutoFill and Private Browsing settings on your device.

On iPhone, iPad, or iPod touch with iOS 9 or later:

1. Tap Settings > Safari > AutoFill.
2. For account names and passwords, check that Names and Passwords is on. For credit card information,* check that Credit Cards is turned on.
3. Open Safari. If the navigation bar in Safari is black or dark instead of white or light gray, turn off Private Browsing. Safari doesn't save account names and passwords when Private Browsing is on.

On Mac with OS X Mavericks 10.9 or later:

1. Choose Safari > Preferences, then click AutoFill.
2. For account names and passwords, check that you selected "User names and passwords." For credit card information,* check that you selected "Credit cards."
3. See if Private Browsing is turned on in Yosemite. Safari doesn't save account names and passwords when Private Browsing is on.

Still need help to autofill your credit-card information?

• On your iPhone, iPad, or iPod touch, tap the credit card field in Safari, then tap the "AutoFill Credit Card" option above the keyboard.
• On your Mac, click a credit card field in Safari to see the message that asks you to choose which credit card to use from your iCloud Keychain.

* Always enter your card's security code manually. iCloud Keychain doesn't store credit card security codes.