I am not sure that your research was very thorough, so I am going to challenge the frame of your question a little bit here. I also observe that you are overcomplicating the issue somewhat - but that's not uncommon. I tried a homebrew druid sub class a while back that, on first review here, was found to be overcomplicated.
There are features and feats that already boost healing.
If you want to boost your healing ability the simplest way is to
Play a life domain cleric
(Citations are from the Basic Rules, p. 25 (same as PHB section on Life Domain Cleric).
Disciple of Life
Also starting at 1st level, your healing spells are more effective. Whenever you use a spell of 1st level or higher to restore hit points to a creature, the creature regains additional hit points equal to 2 + the spell’s level.
Channel Divinity: Preserve Life
Starting at 2nd level, you can use your Channel Divinity to heal the
badly injured. As an action, you present your holy symbol and evoke
healing energy that can restore a number of hit points equal to five
times your cleric level. Choose any creatures within 30 feet of you,
and divide those hit points among them. This feature can restore a
creature to no more than half of its hit point maximum. You can’t use
this feature on an undead or a construct.
Experience: My life clerics used this A Lot.
Beginning at 6th level, the healing spells you cast on others heal you
as well. When you cast a spell of 1st level or higher that restores
hit points to a creature other than you, you regain hit points equal
to 2 + the spell’s level.
You need not expend many, or any, resources healing yourself if you are healing others a lot.
Supreme Healing (if your game gets that far)
Starting at 17th level, when you would normally roll one or more dice
to restore hit points with a spell, you instead use the highest number
possible for each die. For example, instead of restoring 2d6 hit
points to a creature, you restore 12.
When you upcast spells at a higher level, that's a huge boost to healing. Example: 4d6 averages 14, 4d6 with the above feaure is 24.
If you go variant Human for your player race, you can add a feat at level 1.
If there are any official source feats to improve healing, I couldn't
Two of them in the PHB boost healing quite a bit, although the second one relies on synergy with Life domain Cleric to really shine.
Healer Feat. This is extremely useful. Our Tempest Cleric in a Tier
3 campaign (we were at level 14) was still using the second feature on our party routinely.
- When you use a healer’s kit to stabilize a dying creature, that creature also regains 1 hit point.
- As an action, you can spend one use of a healer’s kit to tend to a creature and restore 1d6 + 4 hit points to it, plus additional hit points equal to the creature’s maximum number of Hit Dice. The creature can’t regain hit points from this feat again until it finishes a short or long rest (PHB Ch 6)
That first feature is really nice for getting people up who are at 0 HP. The difference between 1 HP and 0 HP is mechanically significant. You can run, act, hide, whatever at 1 HP. At 0 HP, you are unconscious.
Magic Initiate: if you are playing the life domain cleric, take the Goodberry spell (it synergizes with disciple of Life, so you end up adding 3 points to each one point berry) and two other druid cantrips. (I took guidance and shillelagh). (PHB, Ch 6).
At table experience: this really boosts the pool of HP you can heal your party with between encounters, particularly at low levels. 40 HP per long rest restored, and, your party never needs food since goodberry feeds them.
Temporary Hit Points: an ounce of prevention is worth a lot.
Damage that you and your allies don't take does not need to be healed.
Temporary hit points aren’t actual hit points; they are a buffer
against damage, a pool of hit points that protect you from injury.
When you have temporary hit points and take damage, the temporary hit
points are lost first, and any leftover damage carries over to your
normal hit points. For example, if you have 5 temporary hit points and
take 7 damage, you lose the temporary hit points and then take 2
damage. (Basic Rules, p. 8)
If playing a non-cleric, non-druid class (particularly if they have high charisma like a bard, sorcerer or paladin) the Inspiring Leader Feat offers your allies temporary hit points once per short rest: damage they don't take does not have to be healed.
Each creature can gain temporary hit points equal to your level + your Charisma modifier. A creature can’t gain temporary hit points from this feat again until it has finished a short or long rest. (PHB Chapter 6)
If your bard with charisma 18 at level 4 applies this, the party each has 8 Temp HP. That's damage they don't take and thus don't need to heal during the next combat encounter.
A special shout out goes to the Artificer, Artillerist, who has a Protector option for their cannon that provides significant Temp HP as a bonus action each round. We have discovered in play that this is incredibly useful to the point of approaching overpowered. In one fight at 4th level, I tallied up all of the damage that temp HP had soaked up: it was over 100 HP for a five person party. (Me DM). Once again, damage you that don't take does not have to be healed.
One more spell that I will mention is Heroism. If you are playing a class that has access to this spell, it provides temporary hit points each round - and it refreshes each round. (Temp HP usually do not refresh). At low levels in particular, this prevents significant damage and precludes some of the need for healing
A willing creature you touch is imbued with bravery. Until the spell ends, the creature is immune to being frightened and gains temporary hit points equal to your spellcasting ability modifier at the start of each of its turns. When the spell ends, the target lose any remaining temporary hit points from this spell. (PHB, Spell Description, Heroism)
Caveat: the Temp HP go away after the spell ends. Normal Temporary Hit Points last until used up or a long rest is completed.
Unless a feature that grants you temporary hit points has a duration,
they last until they’re depleted or you finish a long rest. Basic Rules, p. 80)
Play a Druid, Circle of the Shepherd
At 3rd level a very nice healing spell arrives (Healing Spirit), and, there's a spirit starting at second level that provides a temporary hit Points option. See above regarding temp HP. The druid also has access to normal healing spells.
The above is not an exhaustive list, just some of the ones I've seen in play that are very effective.
Bottom Line: you don't need this feat
There are already a number of features, and feats, that do what you want to do: boost healing, and/or prevent damage (which renders the need for healing moot). I suggest that you use them (being new players) and not overcomplicate the game with a feat that isn't built with a solid understanding of the game's balance point. (And this helps your DM out by not forcing them into a play test mode. Your question points out that this is a concern to your DM).
As an aside, I agree with SeriousBri's answer on this feat being out of balance/broken.
Make Use of Short Rest Organic Healing
Lastly: a lot of new players to this edition, and DMs, don't apply the use of Hit Die based healing very effectively.
Short Rest (Basic Rules, p. 70; PHB Chapter 8)
A short rest is a period of downtime, at least 1 hour long, during
which a character does nothing more strenuous than eating, drinking,
reading, and tending to wounds. A character can spend one or more Hit
Dice at the end of a short rest, up to the character’s maximum number
of Hit Dice, which is equal to the character’s level. For each Hit Die
spent in this way, the player rolls the die and adds the character’s
Constitution modifier to it. The character regains hit points equal to
the total (minimum of 0). The player can decide to spend an additional
Hit Die after each roll. A character regains some spent Hit Dice upon
finishing a long rest, as explained below.
Taking short rests, and healing by rolling your hit dice makes for another healing resource that I have seen under used at most of the tables where I have played. When we started out, all of us having played previous editions, that mechanic was not well understood and barely used.
I can't emphasize this enough: as a party, and as a table, become very familiar with the use of HD to heal yourself (all PCs) during short rests. Apply it. Those HD are a healing resource. Use them.