I found an optional rule in the DMG (p. 266-267), called Healing Surges:

This optional rule allows characters to heal up in the thick of combat and works well for parties that feature few or no characters with healing magic, or for campaigns in which magical healing is rare.

As an action, a character can use a healing surge and spend up to half his or her Hit Dice. For each Hit Die spent in this way, the player rolls the die and adds the character's Constitution modifier. The character regains hit points equal to the total. The player can decide to spend an additional Hit Die after each roll.

A character who uses a healing surge can't do so again until he or she finishes a short or long rest.

Under this optional rule, a character regains all spent Hit Dice at the end of a long rest. With a short rest, a character regains Hit Dice equal to his or her level divided by four (minimum of one die).

For a more superheroic feel, you can let a character use a healing surge as a bonus action, rather than as an action.

An additional suggestion: Ask the players to think of how their character uses the healing surge, how it looks/sounds so that 'the sudden burst of regained vitality' also makes sense from a narrative perspective.

Related: Can level 1 characters use Healing Surges since they only have 1 Hit Die?

Gating

One simple solution to your problem is sometimes called gating. You simply require something for an interaction, and your talker (below, assumed to be a Human Fighter) doesn't have it. Here are a few examples:

• The inscription is written in Dwarvish, which the talker can't read. Pass a note to the party's dwarf.
• The party needs to talk to the Archmage, but only members of the Arcanist's Guild can request an audience. Stare pointedly at your Wizard's membership card.
• A nearby urchin might have witnessed your contact's murder, but is too intimidated by the bulky fighter to talk. The child is staring inquisitively at the party's halfling.
• Your Paladin's background as a sailor lets him know that something isn't right about this dockside bar.

None of these are intended to permanently exclude anyone, but to push another character to do something other than follow the leader.

Another variant on this you can use is in the basic formula of D&D: you describe the world, the players describe what they do, and you describe the results. Simply transition from the first step to the second by saying "Rogue, you notice a skulking figure watching the ruckus with interest. What do you do?" At that point, it becomes incumbent on the Rogue to respond, not the Fighter.

Are you sure this is a problem?

Not to put too fine a point on it here, but is this really an issue? Most importantly, is everyone having fun? If you're offering opportunities to your players and they aren't taking them, it's not necessarily anything you did wrong or you can fix.

Spend some time reading DMG page 6, Know Your Players. Different people are looking for different things in a game, and get different things out of it. Maybe your wizard wants to let the fighter do all the talking so he can get back to combat sooner. Maybe the cleric is more interested in fully exploring every map you draw. A different source for similar information is the idea of "8 kinds of fun", which will have several hits in your favorite search engine.

Once you're familiar with those ideas, you can think about your players. Get a feel for what excites each person, and be sure to incorporate a bit of each in every session. If that doesn't seem to be working, you can always outright ask your players what they're interested in and how they feel about the game. Maybe there is brewing resentment, maybe everything is fine. The best way to know is to ask your players.