Is it permissible for me to procrastinate in ending a forbidden relationship, or must I take the initiative to end it, advising the girl who is with me?

You must repent from speaking with this girl because conversing with women without a need is a temptation and a means to evil. You must immediately close all channels of communication with her and leave her a message stating that what you both are doing is wrong and displeases Allah, and that you both must repent to Allah for this matter. Continuing to speak with her will lead to undesirable consequences.