My son has alternaria allergy (outdoor fungus), what kind of allergy medication?

Several possible: Most allergy medications are useful to treat allergy regardless of the cause. In other words, you can take Claritin (loratadine) or Allegra for any allergic rhinitis whether caused by mold, animal dander, pollen, or dust mites. Sometimes the addition of an intranasal steroid medication is needed because of the inflammatory reaction that occurs due to repeated allergen exposure.

Several Options: The treatment of allergic rhinitis consists of avoidance, anti histamines, nasal steroids and allergy vaccine therapy. Some combination of one or all these modalities will be helpful.