Yes God heals today, and does so often.
The end result is always the healing, so whether it's through a doctor or with no intervention is not the point. Since ultimately it went through God and God gives knowledge, provides the right people, and right circumstances. The goodness is still from the Lord.
My faith on healing is shaky honestly. The only exception is if I don't know the person. And the reason is that the fear outweighs the faith. If you have something you're very emotional about...say a parent is sick. Though you believe God can heal them, you also know this world doesn't always go according to plan. So the faith is shaky bc your fear is attached to it. It's a spiritual law.
For example: Imagine you have a dream, and you can fly wherever you want. You tell the other people they can fly too for you know it's only a dream. However they don't believe you. You say hold on to me and I'll help you fly. But they still say no bc they don't trust or believe you, though it's your dream.
So people can heal and also prayer can heal, just as the example.
"Therefore I tell you, whatever you ask for in prayer, believe that you have received it, and it will be yours."