Sync your Photos using iCloud Photo Library.
or you can transfer them to your computer, using this guide:
Sync also Contacts, Calendars, and Notes to iCloud.
When done, restore your iPhone to factory settings, and, at the end, set it up as new.
Follow the steps provided in this support guide:
After setting it up as new, as soon as you enter your Apple ID, your photos, contacts, calendars and notes will be available on your iPhone.
Don't restore it from the backup.