El Capitan upgrade problems help

I upgraded my Macbook Pro from 10.75 to the app store's El Capitan and about 80% of the way through it restarted a bunch of times and had the "Your computer restarted because of a problem" grey screen. Then when it did restart there would be unusual writing over the screen that had a Panic Report and then something about a Kernel after a bunch of jargon

I rebooted it in safe mode. It was a little funky but then actually finished the installation......but now everything is funky and off. Applications are slow and off, etc. When I reboot it, it sometimes doesn't work.

I did a time machine backup before I started the upgrade process, so my question is how do I go back to having a working computer?

1) Is there a way to get this El Capitan to work?

2) How do I reload my Time Machine backup? Does a time machine backup automatically reboot the 10.7 operating system I was on?

(I'm not sure I have the original startup disc anymore, so I am trying to see how I can get my desktop setup to work cleanly without having to do a clean install and wipe out everything...)

My goal is to have a working computer again with my time machine backup but don't know what to do since I was upgrading to a different OS.

Thanks!