I used the aquaphor original ointment which I'm almost 100% certain is the one daniel miller used. But I don't want to give you the wrong information either. Here is Daniel's bloghttp://danielcmiller.com/?page_id=1712
I know there is a video or answer to a question where he specifies exactly which one it is. You'll have to do a bit of research.
In terms of water, no it's not bad getting them a bit wet. I followed Daniel's directions. When in the shower I let the water hit the top of my head and roll down my face, which keeps the lips relatively dry. When brushing my teeth I use an electric toothbrush and I'm mindful not to cause to much trauma to the lip linings with the neck of the brush. A bit of contact is unavoidable. Some toothpastes foam a lot more than others, I use one with minimal foam but we should realise that the toothpastes are not causing this,they may be irritating the wound to a greater or lesser extent depending on how chemically harsh they are. If you have a good layer of aquaphor on before brushing the lip linings will be protected anyway, so the type of toothpaste used isn't really a concern.