Is there any way to increase the number of items I can hold?
Solution 1:
You can increase your inventory size by opening your inventory, going to the Items tab, scrolling down and pressing the "+" at the bottom of your item list.
Solution 2:
If you keep leveling up, you'll get more inventory space eventually. It's not much though. It's like 5 more inventory space every couple of levels.
Or you can pay tickets for it.