What should I do about my situation after the young man I loved proposed to someone else? Is it permissible for me to ask God to make him my destiny and to prevent his marriage to her?

Marriage is preordained by Allah, and one must believe in divine decree and destiny and be content with it. Supplication is a prescribed act and can avert a decree, with Allah's permission, but it must not involve aggression, such as supplicating to prevent a young man from marrying a girl. Rather, supplicate that Allah destines what is good for you wherever it may be, using the Du'a of Istikhara (prayer for guidance). I advise you to fear Allah, for it eases affairs, and part of fearing Him is to cut off your relationship with this non-mahram (definition) young man. Do not pay attention to dreams, as no religious or worldly matter can be built upon them.