How do I transfer my pictures from my current iPhone to my new iPhone without using a computer?

Is it possible? Btw I'm using a new Apple ID so I don't think I'll be able to use iCloud.

As you can't use iCloud, you can try using a 3rd party cloud storage such as Google Drive, DropBox, OneDrive etc. Simply create an account, upload to the cloud, download app on your new phone, login and save the pictures.

Bluetooth

You can't.

You don't