Will to much flea killing application be to much and make a dog sick?

Yes, the chemicals in the treatments can be unhealthy for him if he gets too mcuh of it.

Answer

It is better to work on the source of the fleas in conjunction with flea shampoo. There are sprays available from the vet that interrupt the gestational cycle of fleas. Spray under the bed, in dark areas and vacuum frequently (toss the bag every time you vacuum). Eventually the fleas will be gone.