Things will be fine. The world's medical system is the least of your worries.
What is, is robots that like to take out all emotions and turn you into one of them, creatures that can kill you with one shot and try to kill everyone that isn't like them.
Oh and don't forget a race of reptilian humanoids from the planet Mars! Granted there are more than likely beings of microscopic proportions that could infest their way into the whole of the medical system and try and turn the world's humans into a vegetable state. But that's very unlikely to happen.
And if it does, The Doctor should be able to fix things before too many people die. You'll be fine.