Trout want to stay out of the big flow of water as much as you do. They often times seek out the edges of the creek/river or go behind any object that can provide a break in the current, or they often go to the very bottom of the river where the current is slower.
The water flow has dramatically increased and is moving much faster than normal. Large heavily weighted flies are the rule for muddy water. Streamers like the clouser minnows, big sculpins, or large woolly buggers, weighted enough to hold them down on the bottom, would be my first pick. muddy water flies generally range from a size 2-6. Your flies need to have a lot of rubber legs or marabou, rabbit fur or flash. All of these products have a lot of motion to help trout find them in the muddy water, remember they cannot see as good in the dark water so the fly needs to be right in front of them.
Do not fish light tippet, you will be fishing near and around brush and snags. Remember the fish cannot see as good as normal, this allows you to fish very heavy tippet. I fish 2x-3x tippet in muddy water, that should be more than enough for our trout streams here. Nobody likes fishing high and dirty water, but not all of us can pick all the right days to get out on the water, so if mother nature throws you a curve ball give it a try you may be surprised at the results.