On last adventure my character found an item. Until now I've been buying od DNDBeyond only things related to character's creation so it doesn't show on the list. Does it mean I have to pay real money now to add an item that's been part of the adventure? This feels off as normally I'd just write it down on physical character's sheet. 

You have three options:

1. Buy the content on D&D Beyond. This has always been the case; if you would have to buy a book to access it, you need to pay for it on D&D Beyond
2. Homebrew the item into D&D Beyond using the homebrew tools. This is for personal use only
3. Use the custom item option on your character sheet to add the item directly to your inventory

If the adventure is owned by someone (anyone) in the campaign and Content Sharing is enabled for that campaign then you should be able to add the item to your character sheet.

Yeah, but only if DM owns it on DNDBeyond, not just paper version. 

Anyway- thanks for answers.