I have a DLC item in my inventory, but don't own the DLC?

Solution 1:

According to the Dark Souls 2 Wiki and Steam, Dark Souls 2 Scholar of the First Sin contains all the DLC that have been released since April 1st 2015 (the games release date).

Steam words it as:

DARK SOULS™ II: Scholar of the First Sin includes all the DARK SOULS™ II content released to-date in one package and much more!

The Frozen Flower is automatically given to the player who has the DLC for it. Since you have the Scholar of the First Sin edition, you do in fact have the DLC (and the rest of the DLCs). The DLCs are likely not a separate download since this is an enhanced version of Dark Souls 2, and are probably just included with the game download.