With whatever you have mentioned, there seems to be no sincerity or true love from your cousin. You say that you haven't spoken with him for the last 6 months and he broke up with you; he is back of other girls. It is time for you to analyse whether you want to persuade him and marry him (if it all). Will he be sincere to you later on!
It may not be worth to mess your life because of a person who is trying to avoid you and flirting with other girls. You have to look at all angles in your own interest. Don't keep grouching on the past, begin from where you can begin and move ahead in your life.
Next Steps
Consult a Counselling Psychologist who can work with you and empower you to handle the situation amicably.