Much later in the game, after major advancements in the main storyline, there is an optional quest that if completed will increase how much your character can hold. In the meantime....
Each of the 4 magic vaults at the town halls can hold 24 items each.
If you buy a house for your character, the house will include a permanent storage locker that will hold 24 items.
There are also a couple of permanent storage lockers that are not tied to a house, but one needs to have made a good deal of quest progress to access these locations.
Be merciless with selling loot that is easily replaceable. Loot that is unique or at least hard to get is harder to make such decisions on. But the game does make the concept of opportunity costs part of the game. One's character *can't* have it all. One has to make decisions about what to keep and what to sell and to live with those decisions. At first, the inventory limits drove me crazy, but over time, I've come to appreciate that this is one RPG where one cannot be a hoarder.