Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
Answering your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, states:
Regardless of the insurance issue, your salary in the hospital is for your work. As a doctor in a hospital, your work is halal. Your salary is also halal as long as you give your work with honesty and normal consciousness.
Questioning the income of the hospital is not of your business. It is the business of its owners and shareholders who earn from its actions. You earn from your work.
Besides, the problem with conventional two parties exchange insurance contract is in the non-determined (in advance) obligations of the parties because no one knew when a sickness happens. It is in the relations of the insured and the insurer, not in the fact that the insurance company pays on behalf of the patient. From this angle, it is a pure wakalah as far as the service provider is concerned.
Allah Almighty knows best.