All truth and good comes from God. And God gave humans the intellect and the will to do great things like be doctors. Thus Christians (most anyway) go to doctors because they and their knowledge and skill (given by God of course) can and often are instruments of God.
A relevant example of this is Dr. Ben Carson, who is running for US president and is a retired, world-renowned pediatric neurosurgeon who saved hundreds if not thousands of lives and brought hope and life to the children and their families. He is a faithful Christian who professes that without God he would not have accomplished anything good.
God is the One who saved my daughter's life. How? Because it was Him working through the doctors that found her congenital heart defect. It was Him working through them that allowed her open heart surgery at 10 days old to be successful and it is Him working through them that continues to treat her with love and care. God allowed a bad thing to occur and made good come from it. This experience has strengthened our faith and that of the doctors and also serves as an example of His greatness. Our daughter is a blessing and was a prayer answered by God to her older brothers who prayed for months for a baby sister.