Marrying a woman whom was betrothed by someone

In the name of Allah, the Most Gracious, the Most Merciful

As-salamu `Alaykum warahmatullah wabarakatuh (May Allah's Peace, Mercy, and Blessings be upon you!)

I have a problem that confused me a lot and I hope that you give me some advice:

I am a young Muslim man who is 23 years old. I admired a girl and I made up my mind to marry her. I told my mother and my father to come with me to betroth her. Few months later her father responded with acceptance. I was very happy and I thanked Allah and so did my parents and brethren. However, the problem is: Her cousin proposed to her but her father refused because they had problems in between as his family said. When I heard the news of her cousin, I got afraid to spoil the relationship between them. Satan insinuated evil ideas into my mind -I ask Allah to forgive me-, so I called her personally and we had a short phone call during which I asked her whether I had corrupted the relationship between her and her cousin or not to withdraw my proposal without any problem. She answered my clearly saying: There is nothing between him and me.

What should I do? It is worth mentioning that they agreed that the marriage contract may be written soon; should I rely on Allah and commence marriage?

Could you kindly advise me?

May Allah reward you the best! Thank you!