I live in a two story house, should I avoid the stairs at all costs or can I climb them slowly?

Depends. Depends on your health. If you are 37 and healthy, there should be no reason you can not climb stairs.
Climb the stairs. Unless you have been put on bedrest, climbing the stairs is safe. It is good exercise too. Many pregnant patients enjoy using the stairmaster or elliptical machines at the gym. In general healthy women should enjoy an active lifestyle.