As a Battlemaster, you're more of a tank/controller type than pure damage - and that's probably a great place for you, assuming you have a fairly well-rounded party. The Paladin seems to have consistent damage output covered already, and I'm going to assume you have a Rogue, a Wizard (or maybe a Sorcerer or Warlock), and a Cleric (or Druid) to cover the main four archetypes.
To get one thing out of the way really quickly, Battlemaster only has three maneuvers that use your bonus action - Commander's Strike, Feinting Attack, and Rally. Feinting Attack is particularly good against hard to hit foes - advantage and some bonus damage. Rally saves a friend a few hp. Commander's Strike, however, is probably worth your bonus action every time you use it: either the Paladin gets a free swing with their Great Weapon Mastery, or the Rogue can pull off their sneak attack off-turn. (They're limited to once per turn, not once per their turn, so your Commander's Strike can let them do their ridiculous amount of damage twice as often.)
Your other maneuvers, whichever you select, can do things from reducing damage and allowing counterattacks, to tripping and disarming foes and moving people around the battlefield. It will require more thought and planning than a Great Weapon specialist just wading in and hitting things, but as you reach higher levels, you'll find the ability to control the foes will make you a very valuable ally - and your Paladin will be valued more for their other abilities than hitting a few points harder than you. Don't worry that you're not "doing your job" - keeping the Wizard and Rogue alive and in position do their thing is your thing.
Regarding feats and ability scores: Martial Adept wouldn't be terrible, giving you an extra maneuver per short rest and two more maneuvers known. Dual Wielder is obvious for you, giving you something to do with your bonus action when you're not using it for a maneuver on top of a point of Armor Class. Heavy Armor Master is a great choice.
If you want to focus on your battlefield control, Sentinel is amazing - it's got three effects that all make you a better tank. First, hitting a foe with an opportunity attack stops their movement that turn. Second, enemies can't escape your opportunity attacks by Disengaging. And finally, foes that attack your allies when you're near them also feel the wrath of your opportunity attack. Another controller choice is Mage Slayer - it's more niche than Sentinel, but against spellcasters, you become quite dangerous.
If you're looking for more defense, Resilient (Wisdom or Dexterity) is a pretty good choice, as you're likely to be a prime mind-control target, and caught in the middle of area effect spells often. Offensively, Savage Attacker could increase your damage output consistently without needing to change your build.
An option many melee classes don't consider is Magic Initiate. While you don't have the casting stats for attack/debuff spells, your stats generally don't matter for utility and buffing spells. Although note that many spells require a free hand to cast - but you can always drop a weapon if you need to, or cast buffs before you draw. Just a few sample options:
Druid: Mold Earth (create difficult terrain or low walls to make your squishies harder to squish) and Control Flame (play with light levels to make use of your darkvision or let your allies see further in the dark), Healing Word to save an ally from a distance or Absorb Elements to take half damage from any elemental effect once per day.
Wizard: Booming Blade (uses a normal melee attack, if you hit, the target takes extra damage if they move) and Minor Illusion, Feather Fall, Shield, or Protection from Evil and Good (one ally is immune to mind control from six monster types that have it often, as well as being harder for them to hit).