If a photo is accessible through your "photos" link then it should mean that it's either a photo you uploaded or a photo where you've been tagged or highlighted by someone else. As I have experienced more than once on Facebook, you can also be tagged in a photo where you're not actually in the photo, as a way for that person to draw your attention to an image. I see those as sort of photo tagging spam, actually.

If you uploaded the photo, you can definitely delete it pretty easily, but it sounds like your friend has tagged you in one of their pics, in which case it cannot be deleted, but you can remove the tag.

Here's how you do that.

First off, you probably got a notification when you were tagged in the photo, a la:

When I select that particular notification, I am taken to the photo:

It's a bit hard to see, but on the lower left appears my name, along with "photos" and "remove tag" as links within parenthesis. When I move the cursor over my name, it shows where in the photo my friend has highlighted, e.g., where I appear:

Ha! Last I checked I wasn't a shed, so I'm going to remove this tag by clicking on "remove tag":

Without any confirmation dialog or anything, it promptly removes the tag and the lower left corner suddenly no longer has my name showing:

That's all there is to it, whether a photo is tagged with a dozen people or just you. Once you do that, there should be no path to the photo from people clicking on your "View Photos of Me" link on your Facebook profile.

Good luck!