Using Borax and Baking Soda in a Pool?

Can I use just borax and baking soda in an above ground pool? My boyfriend is allergic to chlorine bleach. We would like to get the pool in the back yard running, but he doesn't want to pay for the expensive baqucil. We would like to use household items to keep the pool balanced. I'm just trying to find a way where we can avoid using chlorine.