Get a 2HB as highest priority, instead of a new Chest.
I can recommend Poison Wind Censer (2HB 20/28). Cheap and a great Weapon.
Using it almost exclusively since level 19 (yes, even before the cap came off) as it was already better dmg than the Slime Coated Harpoon and Springwood Club).
When cap came off at 20 you suddenly hit for like 55 instead of 24 max, damn nice!
I'm maxing my Piercing and 1HB every level (28 atm), but with PWC the mobs die significantly faster than with my 1handers.
You already use SCHW, so you should be set for some great meleeing
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