When saving a PPro project on my external hard drive, it saves as a Photoshop project.

[Pastways]

I have Windows 10 and in the "Open With" command there is no Premier Pro option, Just Photoshop. How do I correct this?

[MyerPj]

It sounds like you should be good to go if it is saved as photoshop and wants to open with PS. ??

Somethings not right with your installation and explanation.

I would suggest reinstalling and using the cleaner as below:

OK, be sure to run the Adobe Cleaner after you uninstall the programs and before you re-install them:
Also, reboot your computer between steps even if you are not asked to...

https://helpx.adobe.com/creative-cloud/kb/cc-cleaner-tool-installation-problems.html

[Jeff Bugbee]

Right click your Premiere project file, choose Properties, Choose change, then scroll down to the bottom and choose Look for Another app, click that, then navigate to your Premiere executable