Even in a win, it's no fun playing against freaking Cho'Gath.
I spectated that match. Yes, it's a hard match-up for Katarina, but you really played laning phase poorly. You had absolutely zero respect for what Cho'Gath can do, or how he does it.
Just as an example, you simply wouldn't stop going for last hits (mostly by Q->W once you fell really behind after the second death) while his Rupture was up (which he was maxing, you should have been able to tell because he was clearing the caster minions in the back by level 6). You'd consistently get minion blocked trying to dodge his Ruptures and get caught.
And it's not like you couldn't dodge them at all. When he'd try to poke you down at range with Q you'd clear it just fine. Just stand off to the side, force Cho'Gath to decide whether to use Q to clear or poke you -
don't let him do both. Do your best farming with Qs at range, let him push up the lane with his Ruptures if he's so inclined. You aren't going to match his wave clear, he's going to make early roaming miserable, so you may as well let the lane push in to facilitate jungle ganks because you weren't killing him without assistance in lane anyways.
You got counter picked hard, you know? Accept that your usually game plan has been thrown out the window and play accordingly as opposed to...hmm...I don't know...Shunpo'ing onto a Cho'Gath surrounded by 5 minions before either jungler has even completed their second buffs when you have <33% health and he has ~40% and his Rupture and ignite are up
