You've already recognized the pattern. Now, when you send her an email, before anxiety kicks in, plan out a realistic anxiety schedule. You tell yourself, "I am sending this now, and I recognize that she might not respond tonight. Or tomorrow. But she usually replies within three days. If she hasn't written back in four days I'll be justified in feeling anxious." Precommit so you're not constantly thinking, "It's been 7 hours. That probably means it's anxiety time, right?"
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.