Under account permissions I have full management. I need to be app admin and to create new apps when necessary. How do assign myself app admin status?

First - if the App Manager is available - you can ask him/her to give you the appropriate access for that specific app.

They can assign you a given role (and/or customize the permissions for that role).
They can give you "Full Administration" access", "Basic Access with Sharing", or "Basic Access"

Sounds like you want them to give you "Basic Access with Sharing" - where you can manage users, but cannot give anybody else "Full Administration" access."

See more here on the online help.
https://www.quickbase.com/user-assistance/configure_role_permissions.html

Alternatively, to become the App Manager - you can do the following

1)  Go to the Account Admin section:  Manage [your account] > Apps
2)  Select the app  (you'll see "Managed by" - which would be the current App Mananger)
3)  On the right, you'll see "Transfer App"
4)  In the "Transfer Application" page - fill in your email address (that you're using for QuickBase) in "Transfer to"
5)  It will take you through a series of prompts.  
6)  At the end, you'll receive an alert on your QuickBase account.  Once you accept the ownership, then you're now the new Application Manager for the app.