Real-world-damage is classified in several different ways in D&D 3.5
Hit point damage
What are hit points? Hit points are your capability to not take the fatal blow, but are also how wounded you are.
Are these two definitions a dycothomy? Well, as with every abstraction I'm prone say yes.
Poisons that only get applied by harming you enemy and drawing blood need HP damage to be dealt. At the same time most other mechanics work really well by comparing HP with how much stamina you still have - when you have none, you can't parry properly and you're k.o.
Cure spells and potions do just what natural healing does, just faster: it restores HP. (Maybe with less scars, maybe with more, who knows?)
Ability damage
This recovers really slowly over days of complete rest (or with specific magic) and I'd go with this to represent having a limb broken, except it isn't specific to a location.
Limb severing
While the game states no in-combat way to have a limb severed, several spells consider the opportunity. Polymorph efefcts have severed limbs take their former form or not depending on which kind of spell or ability you have been using and regeneration (a 9th level spell) is the only way to restore a lost limb save a miracle or some shenanigans involving different spells.
Losing a limb is pretty definitive and shouldn't happen during a combat.
So, breaking an arm does not look like an option.
What would have been the rules-friendly way to handle this? Well, not ruling a broken arm in the first place, and settling for a more temporary form of nonlethal damage, like straining a muscle. Nothing in the grapple rules allows you to disable your opponent that badly. Again, this is a problem that lies in how D&D abstracts this specific thing, and D&D is all about "no consequences until you get to 0 hp and then the only consequence is that you stagger/faint or what have you (a limited list of outcomes that does not match with reality).
Since the D&D rules work like a physics simulator that uses its own unfamiliar phisics, it sure breaks our expectations, but IMO it's better to break immersion where the rules say than having to face unstated consequences like having to decide how inconvenient it is to lose a brawl after it has happened, because the unpredictability of consequences destroys the risk assessment capabilities of the players and makes them unable to make informed decisions.
It'll work, just not the way you described.
Why your plan won't work
In your plan, you are trying to cast two bonus action spells. One is a standard cast of a Bonus Action (Healing Word) and the other is a spell converted from Action to Bonus Action via Quicken (Eldritch Blast.)
Unfortunately, you only get one bonus action per turn.
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.
Therefore your original plan is both not playable via the rules and is a waste of resources. Take the easier path below!
Simplify your plan
The spellcasting rules on page 202 of the PHB state (emphasis mine):
A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven't already taken a bonus action this turn. You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.
Healing Word is already a Bonus Action spell, so that fulfills your Bonus Action cast.
You can them simply cast Eldritch Blast with your Action and all is good. Quicken Spell is not necessary.
But how did you get Healing Word?
Healing Word is not a Warlock option, even as a Celestial. Nor is it on the Sorcerer or Warlock spell lists. As Xirema noted, only the Divine Soul Sorcerer has this, so you'd need that to be your Sorcerer dip (and can only be that dip) in order for this to work as planned.
You could also take the Magic Initiate Feat and pick up Healing Word (if you do, I'd suggest taking it from the Bard spell list to keep your CHA modifier.)
Your actual usage
- Bonus Action Healing Word (1 spell slot + 1 spell point for Subtle)
- Action to cast Eldritch Blast (no cost)
- Above happens in 1 turn
Best Answer
There is no visible effect upon casting Healing Word
Healing word has no language in the spell description that would suggest a visible effect upon casting. In contrast, a spell like Fireball (PHB, 241) states:
Audio recognition
However, there is a Verbal Component to the spell which may be recognized. How that is determined may be table dependent, but Xanathar's Guide to Everything covers Identifying Spells on Page 85.
A DM might also ask for a Perception check (did you hear it?) and/or Xanathar's Arcana check (do you recognize what you heard?) if there is a chance of failure or success. Tables may decide differently if it's possible at all or how to adjudicate discovering that information.
However, a blanket "any creature would see this magical energy and know I was healed" circumvents Xanathar's as well as takes away player agency by removing any ability checks to identify the spell. It's not necessarily impossible or wrong, but by doing so a DM is ruling that this particular creature cannot fail at identifying a spell (as shown by not requiring any sort of roll for success/failure.)
Visual Recognition of Injury
The PHB does give some guidance on Effects on Damage (197)
This leaves a lot of room for DM description and it will be directly related to the damage type as well. The difference between getting to 0HP from Bludgeoning Damage is likely very different than Fire Damage. What the recovery looks like will also depend on how many hit points they received. Something like healing word may only deliver a small percentage of Max HP, and they may not look much different. In comparison, a spell like Heal could completely close up wounds/burns, etc. and the creature looks back to normal (if above 50%.)
Down and out?
In your specific case, I would have asked you to make a Deception (or even Performance) check against their Insight(Or maybe medicine) to see if you successfully "played dead".