Question:
Is there any sites who pays for writing article on medicine/alternative medicine/ ayurveda?

Answer: Don't laugh. Do a Yahoo search for "WHAM forums" or "work at home" and check out some of the online forums. There are a LOT of people who freelance their writing and they apparently love to talk about it. ;-)

You might think about some of the paid blogging sites but, in my experience, those aren't worth the time they worth.

Or think about publishing your own site and selling ad space on it. It'll take a while to see any real money from it, but it can be done.