Thank you for sharing your situation with the Wefugees Community - I am so sorry to read what is happening to you.
Unfortunately, I am not familiar at all with any procedures in the UAE and research appears to be very difficult.
When I try to find any women supporting NGOs in Dubai, the organisation you mentioned and already tried to reach, is kind of the only result I get. I am really sad about the answer they gave you. Only because you are not Emirati, they can not support you!? Very weak.
About applying for asylum: I think there is no doubt that you are in need for (international) protection, but unfortunately I can not give you a clear answer how to apply for it. As I am in Germany and it is difficult for me to make a phone call for further research to the UAE, do you think you may be able to call UNHCR (the UN refugee agency) immediately to get some information on how you could proceed?
These are the contact details for their office in Dubai:
Second floor - Dubai International Humanitarian City Building 4
+971 4 447 5510
Here the details of the UNHCR office in Abu Dhabi:
Al Muroor Road, opposite the main bus station, Al Ladeem St, Al Nahyan Camp Area, Near Emirates College of Technology Villa 54, B2, Abu Dhabi, United Arab Emirates
971 2 66 77 668
971 2 66 76 615
I do not know if there are any possibilities to ask for asylum in an embassy. As far as I know, there are hardly governments in the world, which nowadays accept applications in consulates or embassies.
I am so sorry that I can not help you much for now, but please do not hesitate to get back to us with any further question or update us on your current situation.
I hope you will stay strong and that the circumstances will improve very soon!
All the best,