I suspect that a smart guy like you can figure out ways to communicate regarding this issue in ways that don't come off as clingy. The fact that you are worried about the possibility of "clingy" is some evidence that you aren't at unusual risk of coming off that way (unless there are additional facts in your personal history that suggest otherwise).
In short, something that you come up with after actually spending time (> 5 min) thinking about it is likely to be worth the effort of communicating.
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.