I'd say the data in the linked paper is reliable - it is even in the title (bolded for emphasis):
Diagnosed Allergic Conditions in Adults: United States, 2021
In addition, the methods has this to say (again, emphasis mine):
Definitions
Diagnosed allergic conditions: Adults were considered to have any allergic condition if they were diagnosed with one or more of three selected conditions: seasonal allergy, eczema, or food allergy.
● Eczema: Based on an affirmative response to both survey questions: “Does [Sample Adult] get an itchy rash due to eczema or atopic dermatitis?” and “Have you ever been told by a doctor or other health professional that [Sample Adult] had eczema or atopic dermatitis?”
● Food allergy: Based on an affirmative response to both survey questions: “Does [Sample Adult] have an allergy to one or more foods?” and “Have you ever been told by a doctor or other health professional that [Sample Adult] had an allergy to one or more foods?”
● Seasonal allergy: Based on an affirmative response to both survey questions: “Does [Sample Adult] get symptoms such as sneezing, runny nose, or itchy or watery eyes due to hay fever, seasonal, or year-round allergies?” and “Have you ever been told by a doctor or other health professional that [Sample Adult] had hay fever, seasonal, or year-round allergies?”
So - self reporting from a survey, but needed a positive answer to both questions - "Do you have X symptoms?" and "Have you been told by a health professional that you have Y condition?" before it was considered to be a true case of allergy. This means they purposely excluded self-reported allergies, and that the statistics are likely more accurate than you might otherwise get.
However, this does exclude a lot of people with very common allergies such as allergic rhinitis, where a lot of people will have the symptoms and treat empirically (OTC anti-histamines etc.), but without ever going to see a health professional to get a diagnosis because they likely have the condition and it is easy to treat with widely available drugs. In these cases, would a visit to a health professional for diagnosis benefit the patient? It might eliminate more uncommon problems, but the first diagnostic from the doctor is likely to be [common] allergy - treat empirically and if conditions don't improve, then it warrants further investigation for other conditions; exactly what the patient has been doing themselves.
