In English, medical is medical, which means there is a disease and I have to treat it. But health care means that I am still healthy and need to pay attention to it and not lose it.
If you want to say "medical health care", you can say "Medical Health Care"
I suggest you go to the English website about health care more often, it will help you a lot. I'm not sure if I'm a good person, but I think I'm a good person. If you don't know, you can go to yahoo and search in English.