I'm playing a level 3 paladin and remember reading about spell or class feature that led me add my CHA mod in addition to my strength mod on melee damage rolls, but I cannot find it. Does anyone know what I'm looking for?
No, there is nowhere in the Paladin class feature which adds Charisma modifier to the damage roll.
There is actually a Channel Divinity feature called Sacred Weapon which raises your attack roll, for Oath of Devotion. By activating it, you are granted of attack roll bonus equal to your Charisma bonus (or +1, whichever is higher) for one minute. However, it only increases your attack roll, not your damage roll. If your DM was also applying it to your damage roll, your DM is either mistaken or houseruling.
In higher levels, Improved Divine Smite allows you to add 1d8 radiant damage to all your melee attacks, but that does not depend on Charisma modifier.
Well... do you mind going to the dark side? Because I know of two different ways for a character to get +CHA to damage: Oathbreaker and Warlock. Obviously the latter is not a paladin class feature, but if you feel like multiclassing its an option.
So now you're Evil. Officially. You get an undead army and everything (Control Undead Channel Divinity option, Animate Dead as an Oath Spell from level 9 on). But more to the point of your question, once you hit Oathbreaker 7, you get Aura of Hate.
So not only do you get +CHA to damage, your undead army and/or the undead armies of your Necromancer/Death Cleric buddies will also get +CHA to damage. And also any fiends you may have summoned/bound/allied with. Wonderful happy times ahead for everyone in the realm.
If you prefer a dark hero to an outright villain, are in a high level campaign/know the campaign will get high level, and aren't too attached to any Paladin class features beyond your 7th level Oath feature, you could go for the Warlock's "Lifedrinker" invocation.
So this would really require you to be more of a Warlock than a Paladin, but it does get you +CHA damage (though it's necrotic, so its not great vs. certain enemy types). You still get core Paladin abilities, though (Divine Smite, Find Mount, Aura of Protection, your early Oath features, etc.).
As for flavor, an Oath of Vengeance paladin could certainly forge a pact with one questionable power to help them fight another (By Any Means Necessary, right?). Alternatively, an Oath of the Ancients paladin with a Fey patron makes perfect sense (and does not even really require you to go to the Dark Side to become a Warlock...).
A paladin also has another use for the warlock's recharging Pact Magic spell slots: they work with Divine Smite (Source). At Warlock 12, you have three 5th level Pact Magic slots, which gives you three maxed smites (5d8), or which you can use to upcast a smite spell like Searing Smite (5d6 fire, +1d6 recurring). Complete a short rest and you can do it all again.
Did I mention that these options stack?
Oathbreaker 7, Warlock 12 gives you a bonus = CHA on melee weapon damage rolls, and if it happens to be your pact weapon, you also deal additional necrotic damage = CHA. So with STR 20, CHA 20 (you get 4-5 Ability Score Increases, so it can be done, especially if you're a dragonborn, half-elf, or variant human w/ an ability boosting feat), you deal +15 damage/hit with your pact weapon, and that's in addition to things like fighting style, Divine Smite, Hex, and magic pact weapons.
So if you really want to add CHA to your damage, you can do that.