Answering the question as posed in your title (how to run a game for three players without a healer), you have two main options:
Offload the mentally-taxing parts of running a GMPC
I've played in three groups that didn't have a PC healer. In two of them, the DM assigned an NPC companion character to one of the players. The DM did the majority of the RP for the NPC (e.g., speaking, making out-of-combat decisions, etc), but during combat the assigned player managed the character. This works because combat tends to be the most DM-resource-intensive part of D&D/Pathfinder, and you want your attention as DM focused on that rather than on the NPC.
It sounds like this is your first time DMing, so I'll pass along a general tip: DMing is incredibly mentally taxing. Fun and exciting, yes, but exhausting. One of the many reasons GMPCs are not recommended is because, frankly, the DM already has enough on her plate and adding the responsibility of a PC just makes things more difficult for her.
That said, since you're planning to play at least one GMPC, healer or no: look for ways to offload as much of the thinky bits of playing the character as possible. Reduce the healer's stat blocks to just a healer; I can't remember what the class name is right now but there's a 3.5 healer class that literally only does healing. (Its name might actually just be "Healer".) That's the class one of the NPC companion characters used in my example above, and it made things simple because all his choices were "Who to heal and by how much", rather than tactical things like "heal vs attack vs tank vs control". This reduced the mental load on the DM, plus made it easy for one of the group's other players to take over the NPC in combat.
Use items and skills to make up the difference
The other way to handle this situation is to simply ensure that the players have sufficient Use Magic Device, minor spellcasting, and items/cash that they don't need an explicit healer. This is what we did in the third group I played in without a healer. We were a multiclassed bard/fighter (got some small heals from the bard half, plus UMD); a ranger (also some minor spellcasting, plus general toughness); and a rogue (craploads of UMD, wands, and scrolls). Our DM made sure to drop lots of healing potions and wands as treasure, and to have lots of places where we could also buy healing items. We didn't need a healer because our own minor spellcasting and UMD abilities worked just fine.
Looking at your group's breakdown, you could likely do something similar, since you've got quite a bit of spellcasting/UMD power. Just make sure, as DM, that you drop lots of healing items as treasure. The players will figure it out from there.
You are looking for Contingent Spell.
It comes in both a feat (CArcane) form and a spell form.
You can place another spell upon your person so that it comes into effect under some condition you dictate when casting contingency. The contingency spell and the companion spell are cast at the same time. The 10-minute casting time is the minimum total for both castings; if the companion spell has a casting time longer than 10 minutes, use that instead.
(phb Magic chapter, 'Contingency' spell)
Revivify from the Spell Compendium is probably the ideal target. The affected doesn't lose a level from being revived. A second Contingency (only the Feat can make multiple Contingencies at once), with Heal, would bring him back to full health.
Alternatively, a Delay Spell'd (CArcane) Revivify could be your ticket. Especially if it's cast using Cloaked Casting (CMage) to disguise what spell has been cast. A psicrown containing Anticipatory Strike (CPsi) (GM can explicitly design custom psycrowns), could allow a cleric to cast a delayed revivification as an immediate action right before the last blow is struck.
Alternatively, a custom magic item
A custom wondrous item of Revivify, costing about 1,000gp, that is exhausted when used and is triggered by the wearer's death. It's a custom magic item, but the DM is explicitly allowed to make those, and 1,000gp is about right for a single-use use-activated item of a 5th level spell. Add a second effect (+150% cost of that effect) of Heal to the item, making it cost around 2500gp all up.
Make it only work for clerics of that god.
Item Requires Specific Class or Alignment to Use
Even more restrictive than requiring a skill, this limitation cuts the cost by 30%.
Best Answer
First, I'm going to challenge a presumption you've made. You don't need a healer in D&D 5th edition. It's very nice to have one, but every character can spend hit dice to recover hit points. There is probably a question and answer on this site on the subject.
Next, I'm afraid the only answer to your question is "ask your DM." The only mechanism defined is that skilled hirelings cost 2 gold pieces per day. What skilled hirelings are available and how they're hired is up to your DM.