What is the ruling on my desire to marry a girl I spoke with, even though I cut off my relationship with her because our conversation was forbidden, knowing that I see her in my dreams and she affects me?

By severing ties with the girl, you have closed a large door of fitna (temptation/strife), for the Prophet, peace and blessings be upon him, said: "I have not left behind me any fitna more harmful to men than women," and "Beware of the world and beware of women." What you see in your dreams might be self-talk or the play of Shaytan, so do not pay attention to it and strive to forget about her.

If marriage to her is possible, then it is good, for the Prophet, peace and blessings be upon him, said: "There is nothing like marriage for those who love one another." However, make sure of her religious commitment, her character, her observance of obligatory duties, and her avoidance of major sins. If she is praised in these regards, then propose to her and seek Allah's guidance through istikharah.