I need to repair a well house that has buckling cinder block walls. The well is below ground with a shed above it. The room is approximately 9' x 8' and 8' tall with cinder block walls and a concrete floor. The block did not have concrete poured in it when it was built, the blocks are beginning to crumble and the seams are loose. Would drilling holes in the floor and adding rebar and pouring a new concrete wall on the inside be an acceptable fix?

It is a big band aide, it will help but not really fix the problem. You will be doing a lot of work, at little more and you could rebuild it all the way.