What are the symptoms of an allergy to a Night Blooming Jasmine plant?

Mainly asthma/hay fever type symptoms, but reactions vary from person to person.
http://www.webmd.com/allergies/best-worst-plants

You'll have to scroll down a bit on this, but it does specifically say to avoid heavily scented plants, including jasmine, if you suffer from allergic reactions.

(new link- similar symptoms for flower allergies, different levels as stated already- satguru)

"All parts of the plant are toxic, especially the fruit, and can cause elevated temperature, rapid pulse, excess salivation and gastritis. The nocturnal fragrance can cause difficulty in breathing, irritation of the nose and throat, sneezing, intense headache, nausea and dizziness. Respiratory symptoms have also been reported from close proximity to the flowers."

https://www.childrens.health.qld.gov.au/poisonous-plant-night-blooming-jessamine-cestrum-nocturnum/