The allergins are in the protein in the dog dander. I can't think that baking soda will do a thing!
Vacuum....change the bag....vacuum some more....change the bag....etc.
Mske sure your vacuum has a hepa filter....wipe the walls, just plain water will do. What you want to remove is the "dust" from the animals. It's not germs you are allergic to but the dust....the flakes of skin from the animals.
Removing the carpet should do the job.
Linda C....also an "achoo" person!

Be sure to air the house our after you remove the carpet, perhaps with fans. When we pulled up our wall-to-wall carpeting , we found the padding underneath had deteriorated and crumbled into dust. That dust was awful. I swept it up, then went over the flooring with a wet cloth. And then we had the refinishers come in with their machines to sand the oak planks down, then stain them. The dust was so bloody awful!

Clean the air ducts. Clean any drapes or curtains. If you are removing the carpet yourself, take an antihistamine before you tackle the job.

There is not much you will have to do if you are going to remove the carpeting. After you remove the carpeting, you will want to remove all of the dust in your home. You will want to vacuum the walls, ceiling, furniture, window sills, etc. You will not need to wash the walls to remove "dander". The vacuuming will have already done the job. I have allergies to things in dust, so I make sure that I vacuum the walls, ceilings, drapes, etc. every month. The furniture gets vacuumed every week. What wall washing will help do is remove any oily-dirt the animals may have left as they rub up against the walls. It is important to use a soapy solution, in your water, in order to help break down the oils and dirt.

Thanks everyone for these great tips!