Hi Naomi,
The tmp folder you need should be located in public_html/tmp The one that shows in your screenshot is a level higher than that.
Try adding Admin Tools from Akeeba and having it fix your permissions.
www.ostraining.com/blog/joomla/admin-too...nd-file-permissions/ Also do your upgrade using akeeb admin tools. and if it doesn't change then use it to reinstall joomla. You'll see the button for reinstalling when you go through ugrade.
Also some things you should do just to make sure.
1. Go to Extension Manager > Discover
2. Clear Cache
3. Look for upgrades and install if needed
Go to Extensions > Extenion Manager > Database
I there are any data base errors click Fix.
Go to Site > Clear Cache and clear cache before you check your site.
Clear the cache from your browser as well.
See if that clears things up and let us know.
Cheers,
Ed