Welcome Laura.

David has asked some good questions when it comes to what you consider to be an allergic reaction. It might very well be the dust from the birds that is causing your reaction. Air cleaners really do reduce dust and dander caused by birds.
I know you new ones are afraid and introverted right now, but have you tried offering them bath water or giving them a good shower or spray with a water bottle. This can be very frightening to traumatized birds, but if you can condition them, you can greatly reduce the dander that they produce.
Good luck with them and I hope you get to keep them. You sound like exactly what they need.

We're having a photo contest beginning Oct 1st, so if you have any pictures, please consider posting them! Even if you don't want to enter the contest, we love pictures just the same.

Michael