Hello Ben
If you have a non-OEM Windows 7 Home Premium license that you have upgraded to Windows 10 Home using the same license, the original Windows 7 Home Premium license should no longer be in use on the original computer if you have upgraded to Windows 10.
Regarding the Windows 7 Ultimate upgrade license that you purchased, you should be able to use it on a separate computer as long as the original Windows 7 Home Premium license it was connected to is no longer in use on any computer. Keep in mind that the Windows 7 Ultimate upgrade license will only upgrade a valid copy of Windows 7 Home Premium to Ultimate, so you will need a separate valid license for Windows 7 Home Premium on the second computer where you want to use the upgrade license.