I have Orajel Naturals Teething Tablets and I called the hotline. They said there was no dairy or soy in them and I did not notice a reaction when we used them. I know that is not exactly what you asked, but hopefully you will have similar results, especially since it says it's safe.
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Re: MSPI Quest: Hyland's Teething Tablets
BFP#1 on 02/14/09 BIRTH to Mason 6lb9oz on 10/12/09
BFP#2 on 5/28/11 EDD 2/1/12 Natural M/C on 6/13/11
BFP#3 on 1/20/12 EDD 9/30/12 Natural m/c on 1/27/12
BFP#4 on 4/23/12 BIRTH to Isabella 7lb1oz on 12/19/12