Do you have two-factor authentication turned on for your Apple ID? If you do, be sure that you have another trusted phone number; it can be any phone number you have access to including a friend or relative's Android phone or even a landline. Another trusted device will work as well, but having another trusted phone number is still a good idea. See: Two-factor authentication for Apple ID - Apple Support
If you have that covered, you will be able to use an iCloud Backup from your old phone to setup a new one and you will be able to sync any synced data (e.g., iCloud Photos, Contacts) etc to the new phone.