I'm sorry to hear you're having this trouble with your payment gateways. Honestly, I can't imagine how frustrating it is to go through the process of setting up your store and finding customers and then them not being able to pay you.
Cash on delivery is certainly possible with Shopify. Here you can find the help document on setting it up in your store. Hopefully this will provide a workaround for you.
Payment gateways are determined by Shopify, so I think it wouldn't hurt to send their support team a message and ask what other dropshippers from Turkey use. They might be able to provide some workarounds as well. Sorry again about the trouble, I wish I could help more. Let us know about the COD method!