My two year old has suddenly turned stubborn and it gets every embarrassing for me to handle him in public. Is anyone else facing the same problem?

That's why it's called the Terrible Twos. Your son is at the age where he feels the need to have control over something. I suggest giving him limited choices. For example, if you want him to put on his shoes, instead of commanding him ("Put on your shoes now!"), try giving him a choice ("Would you like to put on your blue sneakers or white shoes today?") http://www.positiveparentingsolutions.com/terrible-twos