Can I sync changes made on MacOS Photos app with Photos in iOS? I am not using the iCloud Sync feature right now. I manually imported all the pictures on the Photos app on MacOS and made some changes (deleted some, updated some etc.). 

I would prefer to not use iCloud syncing as I would rather not pay for storage and the service to sync more than 5 GB of free data.

Is there a way that I can sync the same changes to the Photos app on my iPhone?
Yes - if you opt in to iCloud Photo Library on your Mac - the changes you make to any photo in the Photos library (the main system one - not any extra libraries you create past the first one) sync up to iCloud.

Then on iOS - opt in to the same iCloud Photo Library and those changes will merge up and sync.

Worst case, you'll have some duplicates, so be sure to make a backup of both the iOS device and the Mac library - before you turn this on in case everything gets duplicated.

I have been using this on two to three Mac and 3 to 5 iOS devices without any snags or errors or issues for about 4 years and am quite happy with having my main Photos library stored in the cloud and syncing up / down to all my devices.