Yeah, Siamese (and therefore balinese) are probably poor choices if you have birds. They like high places and can REALLY jump. Also, I'd have to agree with katiemae1277, of my friends that have had cat allergies, the siamese are the ones that they're most allergic to.
Most of those same friends have had less of a reaction to longer haired cats. I don't know why, and can't give you any reason, but a typical Domestic Long Hair seems to bring out less problems for them. I have also heard of the siberian cats being low allergen. They claim it's because they have fewer protiens in their saliva, but to get the effect you have to have a pure-bred.
The Allerpet C really does work. You have to keep up with it though. Also, a good vaccume used fequently helps a whole lot. Finally, you can keep your bedroom "kitty free" which will help with the suffering---my ex was very allergic so I tried everything in the book to get him ok with my little Chester.
Good luck on your search!