Your culture in India is in some key ways vastly different from the majority of many members in the forum (but not all). This is neither bad or good. I find that cultural difference are fascinating...but when it comes to differences such as arranged marriages, there can be a problem trying to grasp it.
Would I be correct in saying that your engagement to your cousin is a parental arrangement?
At some point you may need to decide whether or not you want to break with the traditional custom of arranged marriage. Your cousin appears not be your desired partner. If you continue on this path, you would not likely be happy - a bad situation to enter your adult life.
If you stayed with arranged marriage, would you be marrying your cousin for financial security or approval/keeping peace in your family?