Hi. this is what you do. On the site, click on either the person icon or the message icon. Then on that page on the left, click on my listings. On that page, click on the 'in progress' heading. That will show you the sale that is in progress. I don't have one to check right now but if you click on that, I think it takes you to the sale page for that sale. There should be something that says "already shipped?" If you click on that, I believe it will pop up with a place to enter the carrier and the tracking number. I hope this helps.
Not everything on the site is intuitive but once you figure it out, it kind of makes sense. There are few things you can't do on the desktop, like send offers.
ETA: I think I misread your post. Did you list as if you were going to use their label? You may have to contact them to tell them you didn't use the label.
By the way, they've already deducted the label cost from the money, so whether or not you use it, you are still paying for it. You can't choose after the sale to ship on your own rather than using the label. If you want to do that, you have to cancel the sale.
https://www.mercari.com/help_center/article/117