I keep hearing that this is frowned upon, but I cannot help it. After I share, I circle back and explain how and why I connected the two stories to try to recenter the other person. Is this annoying? How do you want ND people to respond in that case?
Many NTs communicate like thas too, and most of the time won't think anything negative about someone doing it. Like most social stuff, it really depends on context
The situations where I've found it really off-putting is when you've been in a conversation with someone for a while and it's mainly been about them and their problems. If I then try to talk about something that's been bothering me and they immediately go right back to a story about themselves it seems less like they're trying to relate and more like they dislike it when they're not the focus of the conversation and don't care about me. If the conversation has been more balanced up until that point it doesn't come of as so self-centered.
If you're unsure, you can keep the conversation focused on them for a while and then tell your own story after. You don't have to just tell them shallow, stock responses either. You could, and it's probably better, to ask questions about how they feel or their plans going forward or whatever else is relevant to the story.