My list of reasons to refer includes:
1. Allergic rhinitis symptoms that do not respond well to over-the-counter or prescription medications.
2. Allergic reactions to foods.
3. Allergic reactions to stinging insects (bees, wasps, hornets).
4. Difficult to treat eczema that may be triggered by allergies.
5. Persistent or difficult to control asthma.
6. Recurrent or unusual infections that may be a sign of an immune problem.
7. Recurrent sinusitis that does not respond to other treatments.
8. Finally, if someone is struggling with allergy symptoms that may be from a pet (cat, dog, gerbils, hamster, etc.) and would consider having the pet live somewhere else, I would confirm the allergy with testing first.
Certainly discuss with your primary care physician if you have concerns about the above issues.