That's a rough one...from a relationship perspective, I'm not sure how much you can and can't do. Does she have diagnosed anxiety and/or depression? Diabetes has links to both, and can contribute to them, particularly when blood sugar is not properly regulated. (Diabetes basically fucks with your entire physiology, meaning brain chemistry is also affected.)
I can also understand the fear/anxiety about going low, especially if she's had scary experiences with that in the past. The most important things: always have some fast acting carbs (fruit snacks, fruit rollups, glucose tablets, whatever) close by. (Maybe that's something you could help her with?) Test frequently, especially after meals and injections, and make sure you understand how your body reacts to carbs and insulin.
However, chances are that she already knows all of that and the real issue is the mental health challenges. Does she see an endocrinologist? If not, maybe you can help her find a good one that she can explain the anxiety issues with (who can perhaps refer her to another specialist if needed).
Ultimately she has to make the decision to take care of her disease, but that also means she needs to be willing to receive professional help. Sticking around in the 350 range is very dangerous, and without proper regulation she'll likely land in the hospital with DKA (in addition to the myriad of long term side effects). It's probably not a good idea for you to bring that up to her, because I'm sure she knows. Better coming from a doctor than from you.
Anyway, all that to essentially say: try to help her get the professional help she needs. Be supportive of her, but also realize that you can't force her to manage her disease.
