While fishing in murky water can be productive, that's typically with still decent flows, just colored.
If things are truly blown out, a few pointers.
1. Wooded streams stay clearer. If you go to a stream that runs 100% through forest, they never really color up. Farmland streams are the first to muddy and last to clear.
From the initial runoff event:
2. When looking at USGS graphs, after any rain, streams typically have a spike. That spike is runoff, and if in country where it colors up, it will be colored. As it comes down, there's a decently defined spot where it begins to level out, like an L, though never quite 90 degrees. That's the point where runoff is ending and groundwater flow is beginning to provide the majority of the flow. If it was muddy, that's when it'll clear. If planning ahead, groundwater flows will continue to diminish in an almost linear fashion from there for a while. Groundwater flows in freestoners will fall faster than those in limestoners.
3. Large watersheds are the last to come up. That means, when it's raining, the upstream gauges spike before the downstream ones. Small watersheds will come up quickly. Farther downstream, where it's larger, there will be a delay before the effects get severe. To maximize fishing time, during the event itself, pick large water, far from it's source.
4. Small watersheds are the first to come down. That means, in the days that follow a "blow out" event, the first thing to become fishable is your small freestoners, and limestoners near their sources. So following the true deluges look to upstream areas first.
It's all common sense. But it drives home the idea to be flexible. Too many have a favorite spot and just don't fish or wait for that spot to be perfect. Streams don't all act the same, some color up, some don't, some blow out quickly, some blow out slowly, some clear up quickly, others clear up slowly. And in thunderstorm season it's very common for one area to get 2" of rain while another gets only 0.25". Look at precipitation maps!
Be willing to alter your plans and go where it's good!