When you add a repository, press the add clone repository (the one with the green arrow). Then paste the URL of your repo, then type .git in the URL. Initialize the repo, then you should be able to push. Also, make sure your repo on GitHub is public.
It is possible that the repo is set up correctly but Eclipse didn't execute correctly. This has happened to me a couple of times...so just restart Eclipse and it shouldn't be a problem. Or just add a space somewhere in the code and then try commit and push.
When you're adding--or re-adding--your repository, make sure to delete your previous repos on the sidebar. It will save you the headache of wondering which one works!
This video helped me with this process. Hopefully, it will help you too