AppleCare+ and international warranty for iPhone 15 repair in Turkey

There is no International Warranty on iPhone. And AppleCare+ usually applies to the country the phone was sold in. But since you have a clear issue with the battery swelling, visit the closest Apple Store you can attend and ask them if they would be willing to service your phone. There is no guarantee they will, but you really need to ask them.

Please refer to ---> See AppleCare+ Terms and Conditions for complete product details.

Please read this para...(Extracted from the above link)

"Service will be limited to the options available in the country where you request service. Service options, parts availability, and response times may vary. If service is not available for the Covered Equipment in a country that is not the country of purchase, you may be responsible for shipping and handling charges to facilitate service in a country where service is available. If you seek service in a country that is not the country of purchase, you must comply with all applicable import and export laws and regulations and be responsible for all custom duties, V.A.T. or GST, and other associated sales taxes and charges. For international service,

Apple may repair or exchange products and parts with comparable products and parts that comply with local standards."

To complicate matters even more, Turkey in particular has some rather strict regulation regarding regulation and taxation of cellular devices.

Chances are you're going to have to take it back to Japan for service.