How to see a list of applications that I have already downloaded on my new iPhone?

I got a new iPhone because mine was dropped into a pool. Its hooched. When i bought my new one the guy from ATT said there were no found backups OR ICLOUD data. But when I download an app on my new iphone that I also had on my old phone it shows a cloud symbol instead of the download symbol. Is there a way to see the list of apps i had on my old iPhone because i'm having trouble remembering them all. I tried signing into iCloud on my mac but it doesn't show apps.

Sign in to App store on your device. Open AppStore>Updates>Purchased