Recovering data from broken IPhone?

Ok so I broke my iPhone last week and the insurance sent me a new one. The thing is I would like to recover the contacts and messages and photos from my old phone to put them on the new phone but my old phone was not being backed up to ICloud so they re not on there. Any ideas for how I could get my stuff back? Anywhere I could go? I already tried connecting my phone to my computer and going to the Apple Store.

Commonly, you can recover photos, contacts and songs from iCloud and iTunes. But now you can recover them from iTunes if you have made backup before, but this way is risky, and you can't recover them absolutely. Personal suggestion, you can use some recovery tools to get them back. "FoneLab for iOS" does good job in recovering contacts, messages, etc.
Hope you can get them back.

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