Will Apple fix my iPhone without Apple Care?

Yes, but you will have pay for any repairs unless its considered a manufacturing defect and the iPhone is still under warranty.

See here: link-> iPhone Repair - Official Apple Support

With an iPhone 7 it is possible your device isn't even covered under warranty anymore. Use this link to discover what coverage you have:

Check Your Service and Support Coverage by clicking here --> https://checkcoverage.apple.com/