I hate to be the bearer of this news, but there is no such thing as a hypoallergenic cat (or dog for that matter). If a cat has skin, it has dander, and dander is the most common cat allergen. Saliva is another common cat allergen, and all cats have that too.
If you are allergic to the cat you can either take daily antihistamines (such as Reactine, Aerius, etc.) and see if you can tolerate it or find another home for the cat. Reputable animal shelters and breeders will take their animals back.
You may want to see an allergist to confirm a cat allergy (via testing) and set up a treatment protocol.
Otherwise, back pain itself is not a symptom of allergic reaction.