I frequently throw creatures with various kinds of immunities and resistances at my players, and here are some of the ways I plan for them to get around these resistances. Because finding magic items is reliant on the DM, I'm going to focus only on ways that you can get around these resistances without needing the DM to award you anything.
Carry other weapons
If you carry multiple different weapons, you can easily bypass a monster's resistance to one damage type, or exploit a vulnerability to a different damage type. In your case, if you had both a slashing weapon, like a greataxe, and a bludgeoning weapon, like a maul, you could have just swapped to the maul and contributed normally. This also will prevent somebody from crippling you by disarming you of your primary weapon.
Carry weapons made of different alloys
Silver gets around some supernatural resistances, and it's relatively cheap to get an item silvered. Xanathar's Guide to Everything includes rules for treating an item made of adamantine, which can get around the resistances of some creatures, like gargoyles or other such elementals. I had one player who carried around both a silver and adamantine coated weapon at all times, just to get around resistances.
Find a way to make your weapon attacks magical for the purposes of overcoming resistance to damage
There are several class abilities, like those of a Pact of the Blade warlock, or the Way of the Kensei monk, that allow you to treat your weapon as magical for the purposes of overcoming damage resistance. Similarly, Oath of Devotion paladins can use their channel divinity to make one of their weapons magical. You could potentially multiclass to gain these benefits without needing to find anything from the DM.
However, I would not recommend multiclassing though unless you plan out very carefully how your are building your character. It can easily weaken your character as much as strengthen them. Plus, multilcassing is an optional rule that requires DM approval.
Work with your spellcasters
Several classes like Paladin and Wizard can prepare/learn the Magic Weapon spell. This spell requires concentration, but it makes a non-magical weapon magical. Barbarians can't concentrate on spells while raging, so you will likely need to get another player to help you out by concentrating on it for you. My paladin has this spell prepared for exactly this reason; to help me or a party member get around a resistance. Especially since that game has very few magic items.