Healing kits are listed on pg 151 of the PHB (in the general equipment section, not the tools section) and it's text is as follows:

...The kit has 10 uses. As an Action, you can expend one use of this kit to stabilize a creature that has 0 hit points, without needing to make a Wisdom (medicine) check.

So yes, you could possibly use a Herbalism kit to gain proficiency on your medicine check if you don't otherwise have it (this would be up to your DM and available resources), or you can use a Healing Kit (And a use of said kit), to stabilize another creature.

There is also a feat that buffs this kit (The Healer feat)

Ultimately, what I think I would do, would be to allow proficiency with an Herbalism kit to allow for the creation of Healing Kits.

Healing kits are listed on pg 151 of the PHB/48 of BD&D (in the general equipment section, not the tools section) and it's text is as follows:

...The kit has 10 uses. As an Action, you can expend one use of this kit to stabilize a creature that has 0 hit points, without needing to make a Wisdom (medicine) check.

So yes, you could possibly use a Herbalism kit to gain proficiency on your medicine check if you don't otherwise have it (this would be up to your DM and available resources), or you can use a Healing Kit (And a use of said kit), to stabilize another creature.

There is also a feat that buffs this kit (The Healer feat)

Ultimately, what I think I would do, would be to allow proficiency with an Herbalism kit to allow for the creation of Healing Kits.