Hi A.,
The tooth could be the culprit, that was the case for us for quite a while.
But, since there are so many other things going on, i'd take it one step at a time. milk allergies usually come in rashes and hives, blood in the stool. Until she is regular again,take away the milk, give her plenty of poop stoppers (rice, applesauce, banana) don't worry about nutrition, just hydration! And then, when she is healthy again, try the milk unless you saw any of the reactions described above. If you saw those, take her to the doc. They can do a whole series of allergy tests on her skin which won;t affect her digestive system.
Good luck,
M. (mother of 2 boys, 4 and 2 years old)