My Garden's been INVADED!!!

To look at the ground in my garden you would think it was very sandy...wrong it is actually red clay that has been invaded by ants. Every where you look the ground is moving and I do mean everywhere! Front and back. Ant hills around the gates as if they were guarding the property.
The hills around my flowers are several inches high.
I try really hard not to use chemicals (I have severe chemical sensitivites) but I donned a mask and sprayed the the entire property with an ant killer.
I couldn't plant seed in the veggie bed because the ants were all over.