Does your medicine skill affect the amount of heal you do to your companions too?

I would assume so.

I think I remember reading somewhere that Pack Rat will cause a bug where when you move ammo to a companion's inventory, it'll treat the item as if they have Pack Rat when you initially move it, then it will recognize they don't after the transfer. This means you can actually give them more ammo than they carry (for example, your 230 pounds of ammo with Pack Rat will be accepted by Boone, even though in reality, that's 460 pounds of weight for him. It won't stop him from moving though). Just based on that, I'd assume your medicine skill and perks would increase the amount that stims heal for companions.