Every single generation you make in Midjourney (even if you are private messaging the bot) is publicly visible on the Midjourney Gallery Web App.
What's more, anybody who knows your Discord ID can use it to find your Midjourney profile and see every single generation you've ever made.
Don't want that to happen? You can make all images private. But you will need to upgrade to the $60/month Pro plan.
You can see what plan you're on or upgrade plans by messaging the Midjourney bot the command:
Midjourney will send you a message with a button: “Open subscription page“. Click on this.
Scroll down to the plans. You'll see which plan you currently have.
Upgrade Plan button under Pro Plan:
You will be asked when you want your plan to change. If you choose to "Swap immediately", or current fast hours will be added to the new month.
Now that you are on the Pro Plan, you can activate stealth mode.
Message the Midjourney bot:
--private and your generations from now on will all be private.
To make existing generations private, login to the Web App.