I wouldn't overthink this. A writer is a thinker who puts words down to share with others. (As opposed to an author, which I personally define as a writer who has sold some of their writing.) What you wrote in your initial post is writing which conveyed and idea which we have been engaging with in this thread. Congratulations! You are already a writer!
When I got started writing fiction, I prayed a lot about what God could do with my writing. I have written non-fiction (forum posts, FB posts, think pieces, technical writing, memoir pieces, all that stuff) and fiction (short stories and longer - my current WIP is over 171k words). Some things I write explicitly for Christians (to encourage, entertain, educate), but most of what I write if for 'normal people'–scripture says the fields are white and the workers are few. I write from a Christian worldview for the larger audience, and therefore my writing carries my belief system but isn't thinly-veiled preaching. I'm telling stories where people make decisions and their actions have consequences. We frequently look at Tolkien and Lewis and the effect their stories had on the larger world of readers, both Christians and non-Christians.
I think I'd ask God to help you to know how to use your writing. It entirely acceptable to write just so you know what you think about things. However, it's possible He has a use for your writing to a larger audience. I read a story the other day about a man who worked in a small bank in Ohio with lax security in the 80s. He told him a story that he could get away with walking out of the bank with a large sum of money, and nobody refuted his story. So one day he did just that, and walked away with sum equal to $1.6 million. It is said 'rationalization is the second strongest human drive,' and I believe that. I've talked myself into so much trouble. I bet you have, too. This is why storytelling is so important–people make decisions based on what they think is the truth, and the 'truth' he told himself was 'I bet I could walk away with a lot of money,' and he did.
But while he never got caught, he didn't get away with it. He ran and started a new life and lived a lie for 50 years, but was haunted by guilt for his entire life, and he finally came clean
on his death bed. The stories we tell ourselves inform our choices, and those choices have consequences. The world is telling people lies, and those lies cause carnage, sometimes leading to death, and sometimes far worse.
We have the ability–and I think the responsibility–to use our words to tell the truth in a way people can accept or appreciate. Sometimes, that's through a sermon or an essay, and sometimes it's through fiction: 'Once upon a time, a man found himself at the very brink of death, and cried out for help.' Stories resonate with people. What we write matters, and we're here to learn to write better so our stories (both fiction and non-fiction) can reach people who need to hear them.
To sum up, yes, you're a writer, and you're in good company here.