Facebook – How to Hide Activities on News Ticker

Facebook keeps on performing some sort of A/B testing, where few users (based on some business logic of facebook) will see one UI, while rest will see other UI.
I don't know how it could be possible at the time this question was posted, but currently you can give a try to these steps:

1. On sidebar of the homepage, you will see 'triple dot' next to News Feed link.
2. Click on this. If you don't have this option, it means right now this feature is not available to you.
3. You will see multiple options here, like:
   i. Prioritize who to see first: Select names of friends whose posts you want to see on the top of your timeline.
   ii. Unfollow people to hide their post: You can unfollow your friends right from here, so that their post will never be displayed on your TL, unless you follow them again.
   iii. Reconnect with people you have unfollowed: If you had previously unfollowed someone, you can refollow them right from here.
   iv. Discover Pages that match your interest: Relevant pages based on your activity will be suggested by facebook. Click like to get their notification.
   v. See more options: If you have any hidden apps then you can manage them from here.
   
   Please have a look at the screenshot:
   

Are you referring to your News Feed (Top News), News Feed (Most Recent), or the Recent Activity on your profile?

I think that News Feed (Top News) only displays what Facebook considers to be most interesting to you, so I wouldn't expect your own likes/comments there. The News Feed setting that you mentioned applies to the Most Recent setting.

News Feed (Most Recent) does not display individual stories for comments and likes on posts; you would only see them under the corresponding post, if it is expanded. Are you saying that you expanded the likes/comments and you can see comments from other people but your comment is not there? Sometimes it takes some time for it to show up although it shouldn't take days (unless it was deleted).

If you are referring to the Recent Activity on your profile, there is an additional setting for that that you didn't mention. On your profile's Wall (not your News Feed), scroll to the bottom and click Edit Options. If you have hidden any kinds of stories from your Recent Activity these will be listed and you can unhide any of them by clicking the X and then Save.

As for the Photos tab, that used to be a known issue although the link to Facebook Help in that answer does not seem to work now. I don't know if that means that it should be fixed.