There is a Lawn Care forum that will be able to advise you on redoing your fert and reseeding.

If you add photos that show more of the area, including your home and the grading at the corner and behind your back yard, people here will point you in the right direction.

April

The second picture clearly illustrates that your yard is not properly graded, such that grade slopes down from all faces of the house for several feet, the (usual recommendation being 10'.) A shallow swale running parallel to the house, should be created between the fence and the walk. (It should not look like a ditch. It should be almost imperceptible to the eye ... just enough to maintain proper drainage.)

Since you had just removed the large rocks prior to the storm, the raw soil underneath was vulnerable to washing. It's a matter of persistence in getting turf reestablished before rain wash soil away. It would be quicker and easier to establish sod, if it will take in your area this time of year. If you use seed, you'll have to keep reseeding each time it is washed away. If you keep it up, eventually you'll win.

I wondered if the wood or rocks on your neighbor's (?) side of the fence and the wood chips or slope to the rear of that are causing problems. Is there a low spot, a swale, beyond the long piece of fence?