Even if you could run over to stimpack them, I believe in hardcoe mode they won't instantly heal them, just like they don't instantly heal you.
Give your companions better armor. If you leave them in their default 2-6DT clothes they can be fragile in melee range, especially early on when their clvl & hit points are still low. Don't let them get swarmed, because while companions are often crack shots, they're not generally geared to being super-tanks, unless you have a very high charisma + give them high DT armor. Put stimpacks/aids into their inventory, they'll occasionally use them on their own (but not all the time).
Mostly...if you don't like nursemaiding them in hardcoe, don't use them. Also, Lily is far away on a mountaintop beyond New Vegas/The Strip, and the others require doing some quests or combat to acquire. Arcade in the Mormon Fort can be had early without his high speech checks if you have an INT of 2 or less.