I’m trying to trade our old phone in but can’t remember the password for screen time and I’ve tried everything! I’m even more annoyed now I can’t remember the password for my new phone either! I never did that for this one

If you have forgotten your Screen Time passcode

Use this link to reset your passcode If you forgot your Screen Time passcode - Apple Support

If you are unable to reset Screen Time passcode from the this-> link then, you will need a computer. If you don't have one, borrow from a friend.

Forgot? Click below to reset…

Click->If you forgot the passcode for your iPhone, iPad, or iPod touch, or your ...

Regarding your data, If…

1. You have an iCloud or iTunes backup, I am sorry there is no use of a backup because if you restore from your backup your Screen Time Passcode will be back. 
2. You have synced your data to iCloud, then what you will get back is what you have synced to iCloud and uploaded to iCloud Drive; like the information that are synced and stored in iCloud are, Contacts, Calendars, Bookmarks, Mail, Notes, Voice Memos, shared photos, iCloud Photos*, Health data, call history, and files you store in iCloud Drive. (*-If you had turned on iCloud Photos, your content is automatically stored in iCloud.)
3. You have imported your Photos & Videos to Mac/PC then they are safely residing there
4. You have uploaded some of it Cloud Drives using Files app (iCloud Drive, Google Drive, OneDrive, DropBox, Flickr, box, AmazonDrive, Adobe Creative Cloud etc)
5. You have not imported nor you have synced nor uploaded your data to cloud drives prior to forgetting the Screen Time passcode then I am sorry, all your data is lost.

For your old iPhone that you have forgotten your Screen Time password, If you can't remember a restrictions passcode that you set on a previous version of iOS, or you forgot your Screen Time passcode, then you need to erase your device, then set it up as a new device to ➔ How to remove the passcode.

For your new iPhone that you have forgotten your passcode, You will need to reset the passcode on the iPhone. You will need a computer to complete this task. You can reset your passcode by following the instructions in this article by Apple ➔ How to reset your passcode on a disabled iPhone. All your data on your iPhone will be wiped clean in the process.

Axel F.