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:
A bright streak flashes from your pointing finger to a point you choose within range...
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.
If the character perceived the casting, the spell’s effect, or both, the character can make an Intelligence (Arcana) check with the reaction or action. The DC equals 15 + the spell’s level. If the spell is cast as a class spell
and the character is a member of that class, the check is made with advantage.
This Intelligence (Arcana) Check represents the fact that identifying a spell requires a quick mind and familiarity with the theory and practice of casting. This is true even for a character whose spellcasting ability is Wisdom or Charisma. Being able to cast spells doesn’t by itself make you adept at deducing exactly what others are doing when they cast their spells.
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)
Dungeon Masters describe hit point loss in different ways. When your current hit point total is half or more of your hit point maximum, you typically show no signs of injury. When you drop below half your hit point maximum, you show signs
of wear, such as cuts and bruises. An attack that reduces you to 0 hit points strikes you directly, leaving a bleeding injury or other trauma, or it simply knocks you unconscious.
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".