When you update your Nikon cameras firmware many third party lenses will have auto focus problems or not even work at all.
The most simple fix is to revert back to your last camera firmware when the Sigma lens still worked correctly. Another option is to upgrade your Sigma lenses firmware by way of the Sigma USB Lens Dock. You can also take you lens into a Sigma dealer and pay them to update your lens to the latest firmware. Some dealers charge around $15 to do the update.
All of your Nikon lenses should still work correctly after your D5500 firmware update. If they don’t work correctly like the Sigma lenses you have a different issue.