Even though I don't have an eating disorder, I found a CGM extremely useful. It seems odd that the diabetes nurse would dismiss your request out of hand in the circumstanes. But I guess she's not an eating disorder nurse (for want of a better word). But I think it would be worth getting a letter from your phychiatrist to give to your doctor (not the nurse) for them to see the bigger picture, not just in terms of your diabetes, but also in terms of your mental health and related conditions. Good luck for a positive outcome.