Obviously after a visit to the dentist
and an allergic reaction
a few hours later, you are dealing with allergies due to various allergens (depending on the exact circumstances) such as:
1. latex gloves - usually used for examinations
2. antibiotics - if given before procedure
3. aspirin or NSAID based gargle or mouthwashes
5. local anaesthetics
Keeping in mind the above possibilities, your dentist now needs to exclude which ever ones he thinks not possible (as your daughter was not exposed to) and a skin prick test should be the follow up test after this. Latex allergy
can be checked with a blood test
for specific IgE and so can chlorhexidine.
I hope that was useful.