Can I just delete my photo library on my mac? I only want those photos on my personal iPhone.

You can delete the Photos library and never use Photos on the Mac. If your Photos library is empty, there's no real reason to delete it. If the library has pictures in it, be sure you don't want them. The best plan would be to delete the library-- no need to delete pictures before deleting the library. Personally, I'd make a backup of the library-- you never know...

If you're library and your iPhone are connected to iCloud, then deleting the Library will not affect the pictures on your iPhone or in iCloud.