Hmmmm... That is strange! But adults can develop allergies to things that they had no problems with before, so it is certainly possible. The watery/smelly stool could be explained by teething, but the vomiting isn't so easy.
Allergies are easier to detect by blood/skin tests (because they are an immune reaction), while intolerances are mostly discovered through food eliminations because testing is more invasive. So in your case, you would eliminate dairy from her diet completely for a time (in general, it takes 2 weeks to completely eliminate the offending proteins) and if her symptoms disappear then you would suspect an intolerance. If you are unsure or want to confirm, you would reintroduce dairy and see if symptoms return.
Not to oversimplify, but could she have not been feeling well? A virus or something? I know that Dylan has thrown up his soy milk before when he was ill (not with a V&D bug, just fever and generally unwell) and the health nurse I spoke too said that milks (other than breastmilk) can be very difficult to digest and that what happened to Dylan wasn't unusual or really a cause for concern.
Hoping some other moms jump on with ideas too!