Which Fungi / Molds are Allergenic?
In general, all molds are capable of being allergenic (if present and inhaled in a large enough quantity or it can also depend on the length of time of exposure). Like pollens, mold spores are important airborne allergens only if they are abundant, easily carried by air currents, and allergenic in their chemical makeup. 

Found almost everywhere, mold spores in some areas are so numerous they often outnumber the pollens in the air. Fortunately, however, only a few dozen different types are significant allergens.

In general, Alternaria and Cladosporium (Hormodendrum) are the molds most commonly found both indoors and outdoors throughout the country. It is believed that Cladosporium is the leading mold allergen. Aspergillus, Penicillium, Helminthosporium, Epicoccum, Fusarium, Mucor, Rhizopus, and Aureobasidium (Pullularia) are also common. 

When inhaled, microscopic fungal spores or, sometimes, fragments of fungi may cause allergic rhinitis. Because they are so small, mold spores may evade the protective mechanisms of the nose and upper respiratory tract to reach the lungs

In some individuals, exposure to these fungi also can lead to asthma or to a lung disease resembling severe inflammatory asthma called allergic bronchopulmonary aspergillosis. This latter condition, which occurs only in a minority of people with asthma, is characterized by wheezing, low-grade fever, and coughing up of brown-flecked masses or mucus plugs. Skin testing, blood tests, X-rays, and examination of the sputum for fungi can help establish the diagnosis. Corticosteroid drugs are usually effective in treating this reaction; immunotherapy (allergy shots) is not helpful.