Hi Arashi,
It sounds a bit like the speed at which your boyfriend is trying to move at is a bit overwhelming for you. I understand why you are getting slight anxiety attacks, but don't feel like you need medication for them - you know what triggers the anxiety, so let's work on that!
There's been some good all-round relationship advice here about making sure you feel comfortable, but you already instinctively know that, which is why you posted in the first place.
So here's a thought: I am going to assume that it took your boyfriend quite a while to become interested in diapers - it doesn't usually happen overnight (for me it took probably 3 full years of questioning myself before I first even looked at an adult diaper). So, maybe ask him how long it took him for the desires to become established, and then say:
"I probably need at least that amount of time to get to the same point."
Hopefully that should be logical to him? That won't stop him from being impatient, but at least it will give him a reason to give you breathing space. My gf is into light BDSM - she likes being held down, tied up, handled roughly, taken by force, that sort of thing. I can't stand doing any of those things, I am a gentle buttercup at heart and I hate hurting people even slightly. But I have taken a year or two with her and slowly opened up to trying it all with her. She loves it! I don't. I needed time to get my heart around the fact that I was hurting her, but she liked it. I still have problems with that. But as I explore this side of her, I find that she falls more and more in love with me, which for me is totally weird. I. Don't. Do. Abuse. In. Any. Way.
Anyway, maybe keep reminding him that you need the same length of time that he took....? I hope you find your way with this xx
EDIT: Anxiety isn't always bad, btw. It's flip side is excitement, they are basically the same emotion, but one has "bad" attached to it, and one has "good". Maybe to help your anxiety, you can start a process of desensitizing yourself to wearing diapers? As I wrote above, it took me 3 years from the first time I looked at a sanitary pad (and nearly died of anxiety, I'm not kidding), to being able to buy them at the supermarket (still nearly died, but at least I could do it).
If you take a cute pullup, for example, and leave it in your own room, for you to study, look at, feel, watch, think about, check your emotions for a little while, you may find that you are able to process why you get anxious, and so that anxiety will subside a little.