would this piss you off?

I cry super easily like yesterday I cried about trees and I can't even figure out why. Anyway one thing I'm pretty insecure about is that when friends tell me what they've been through I cry really easily. I try really hard to hold it in because I don't want them to think I'm trying to make it about myself or that I'm being dramatic or something but sometimes it's impossible. So I wanted to ask if when you're trying to talk about something you've been through would you find it annoying if the person you're telling starts crying before you can finish?