Have you dated before?
It sounds like these contact points are natural accumulation points for your anxiety - not so much that you're specially anxious about them.
That said, what sorts of things are you requesting? I'd recommend a shift to make suggestions, or invitations where a 'no' answer can very clearly (even to you) be accompanied by 'It's sweet of you to offer, though' rather than 'GTFO'. If requesting something comes up so often that you've noticed the pattern, and they cause an aversion, perhaps you should avoid making so many requests per se?
I have dated before, but not much. The most significant relationship I've had, I sort of begged her to go out with me (to be fair to myself, I was pretty convincing), moved to another city to be with her, and was "contracting" as a job which really meant sitting around websurfing all day. There was no structure in my life and I couldn't hold things together, and after a few months she decided to break up with me and move 1000+ miles to go back to school. This was a formative experience for me and I'm sure it's related to my current anxieties.
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.