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?

Yes yes. This phase can be the most difficult to handle. Kids are learning to say no, do the exact opposite to annoy you. I know it’s easier said than done, but you will have to be more patient and try not to react to his antics. That way he won’t get motivated to do it more to gain more reaction. Best way out is to distract him to something else instead of saying no. All the best!