Multi-class to Warlock.
The OP's question is asking how they can be more competitive in terms of damage output, while still using 2 daggers. Since using 2 daggers generates the potential for 8 points of damage (+ bonuses) each round, one way to increase this amount would be to multi-class to Warlock.
The Warlock class gives you access to the spell Hex.
Until the spell ends, you deal an extra 1d6 necrotic damage to the
target whenever you hit it with an attack.
At 1st level, a Warlock can cast this spell once per short rest and it lasts an hour at a time. This spell increases your potential damage output to 20. At a maximum (before bonuses) of 10 points of damage per hit, that's more raw damage potential than any other one handed weapon in the game.
Granted, because it's a concentration spell, it's not ideal for someone getting hit a lot - but, realistically most mobs should ignore you and your daggers to focus on the giant barbarian with the great axe.
@NautArch brings up an excellent point in the comments below. It's worth noting that Warlock isn't the only class with access to an ability that adds damage dice to each attack. However, in the case of the Ranger's Hunter's Mark and the Paladin's Divine Favor, multi-classing would be less favorable since neither class gets access to their spells until 2nd level.
Another alternative, as mentioned by @RevenantBacon, would be to take the Magic Initiate Feat to gain access to the Hex spell. The downside here is that you'd only be able to cast it once per long rest and it would take up one of your Ability Score Increases if you weren't a Variant Human, but you wouldn't have to sacrifice a level from your main class to do so.