Transforming my data into my new iphone

I heard that even if you delete photos, contacts or notes they will still be in the iphone. I got a new iphone and transferred all of my pics, notes, messages, apps and contacts to my new one from my old one. Will the data i deleted from my old iphone be in the new one?

Probably not.

No, the deleted files won't get moved to the new phone…
The deleted data has some traces in that phone… These are based on the memory location in that phone, which can't be copied.