I just need to know how long should I give this no contact thing, given our relationship was only a month.
Accept that she is not ready for a relationship, and simply move ahead with your life. She needs a lot of time, and space, so give it to her. I think she got into a relationship with you, and moved to fast, before she was ready. Sorry guy, let this one go. Keep NC, until you can accept her as a friend with no other expectations.