Maybe I can just try not to request things over email or text message?
Yes. That's a good idea. It's best to talk in person where you can see the bodylanguage of the other person and can see their emotional response to your request.
If you feel anxiety about your request and your girlfriend is empathic, she can help you when she sees you being anxious.
I started going out with a fantastic girl a couple of weeks ago. Everything is great, except that whenever I've sent her a text message or email requesting something and haven't received a response yet, I experience significant dysphoric anxiety, fearing that her response will be not just "no" but "no and I don't want to date you any more". This is due to brain chemistry or personal history, take your pick—either seems like a possible explanation to me. But there's certainly no evidence supporting the idea that this is likely to happen, nor is the anxiety helping me prevent it or helping me in any other way.
Does anyone have evidence-based advice, or pointers to same, on dealing with this kind of issue? It is the only splotch on what have otherwise been the best two weeks of my life.