Woots! That's good calibration right there! I think you're going to be fine. =]
Also, I don't know what types of requests you were talking about, but if they're about making plans, a nice trick is to sometimes say "Can you please let me know by [day, time]?" That's not weird or clingy because everyone understands (or at least they should) that people are busy and need to know stuff to plan out their schedules. So you have some control over the time window in which you feel anxious. If she doesn't respond in that window, then assume no (like the pocket veto!) and do something else!
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.