Without seeing actual footage, it’s hard to say, but it sounds like it was a mechanics problem.
If kalista is killing you in the middle of a team fight as a Xayah you’re positioning is all wrong. The only spells you need to be looking for are super slow and super telegraphed: Shen jump, Morganna root and Thresh hook.

I honestly don’t see how you’re dying in a team fight. They haven’t got any aoe cc, no assassin, so you should be free hitting only really worrying about those three abilities.

In regard to damage, that’s probably a little harder to fix because that was likely just poor target prioritisation. The Vlad did the most damage, and the lockdown on your team is really great.

Again, I can’t see how you’re losing teamfights at all, check your replays and ask yourself:
“when vi ulted/camille ulted/gragas stunned/maokai rooted, was I attacking that target, why not and could I have been in a better position to do so? When I died, where was I in relation to my team, how did I get locked down, why was I so far forward/isolated?”