On Facebook, I noticed that the comments and likes for a photo I checked in are not showing up on my profile but they display when I click into the photo.
How can I get them to display directly on my profile?
The likes and comments on the photo visible in your profile/timeline because of you being tagged there/checked in/you shared that photo is one thing.
And the likes and comments on the actual photo (in the Facebook Page or Facebook Profile of the actual up-loader) is a completely different thing.
When you click on the photo in your Profile/Timeline, you go to the kind-of-full-screen-view-of-the-actual-photo.
In your Profile/Timeline you will see only the likes and comments that people posted on the photo through your Profile/Timeline (by visiting your Profile/Timeline). Also these likes and comments are not added to the actual photo.