Rash, breathing. Dextromethorphan can cause direct histamine release, resulting in a rash, nausea, dizziness, and breathing difficulty. At high doses hallucination are possible.
Not likely. Delsym (dextromethorphan) can cause adverse reactions in some people, such as nausea, dizziness, fatigue or abdominal pain. These are infrequent in nature. I am not aware of any cases of dextramethorphan allergy.