D&D 5E (2014) Would You Allow This Spell?

No.

It's a reaction that deals a ton of damage and is triggered by your own combat damage.

Hellish rebuke is a defensive version of this and at 3rd level deals 4d10 damage.

DMG guide on spell creation states a single target spell should be 5d10 damage if that's all it does. When combined with other things, it should be less. So the damage is too high.
 

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It its probably balanced but No. because It looks like a smite, smells like a smite, deals damage as a smite and pretends not to be.

I would chance its casting time to bonus action. damage only on a hit. Migth allow for multiple targets if one has extra attack or haste going on but not more then once/target. OR reduce damage and apply to every attack. (but than this is no longer a single target :P)

Searing Blade
3rd level evocation
Casting time: 1 bonus action
Duration: 1 turn.
Until the end of your turn, whenever you hit with a weapon attack it deals additional 3d6 fire damage.

If you really want the single target going

Fiery Assault
3rd level evocation
Casting time: 1 bonus action
Duration: 1 turn.
The fisrt time you make an attack on the turn you cast this spell, flames engulf your weapon burning the target of the attack. Wether you hit or miss, the target takes 8d6 fire damage, or half of that if it succeds on a Dexterity saving throw.

I would keep ranged weapon a possibility (becase archers need fun things too). dont see much problem with a sorcerer getting it or a Eldrith Knigth/Elemental monk really. wizard would probably not have on its list though. If an bladesinger/warwizard/specific PC wanted it could to do the research for that spell on downtime, creating or learning fom a sorcerer/martial artist ;)
 

I found a 3pp Sorc/Wizard Spell.

Level 3 soell
If you hit someone with a melee attack you can cast it as a reaction.

It deals 8d6 fire damage save for half.

Single targets fireball keyed off a melee attack.

Nastiest scenario I can think of is bonus action shadow blade, cast green flame blade have an attack then cast this spell.

That's slot if damage for a sorcerer.

You cant cast more than one (non csntrip) spell in the same turn.

That includes spells cast as reactions.
 

The standard way 5e does this is like the smite spells - bonus action cast, takes concentration, goes off on hit. No extra save needed.
 

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