The goosegrass and dollar weed are most important because they will choke out the St Aug. Spray them with Weed-B-Gone formulated for St Augustine. Ask for the right one at the nursery. That product should not hurt the grass. Sledgehammer for the nutgrass might help. Just going to weekly watering will help because nutgrass likes it really wet. Mowing higher might help. Around San Antonio the new recommendation for nutgrass is to spray molasses on it. They say 1/4 cup per gallon, spray the leaves and drench the soil. Molasses always has to do with the microbes in the soil, but I don't know what they might be thinking.

Hard to tell but it looks like there might be a different grass in there.

Those are weeds. Dig them out before you have 10 or 20 or 100 of them.

If you had not already applied a chemical fungicide I could have helped you. Recheck the label on your fungicide to be sure it works in the temperatures you are getting now. Most tell you to not use above 80 or 85 degrees F. If that's on your label then stop using it now. The easy solution to the problem, had you not already used the chemical, is to apply ordinary corn meal at rate of 20 pounds per 1,000 square feet. If you cannot find corn meal in 50 pound bags at your local feed store, you can also use cracked corn or corn flour from the grocery store. You can find it in 25 pound bags in stores that cater to the Hispanic community. Corn meal works by attracting a beneficial predatory fungus which kills the disease fungus. So if you have already used a fungicide, then the beneficial fungus is gone. If the temps are too high for your chemical fungicide, then wait 2 months and try the corn meal. Or you might be able to speed up the recovery by using compost at a rate of 1 cubic yard per 1,000 square feet along with the corn meal. Compost contains the beneficial fungus you need and will reinoculate the soil with it. Here are before and after pictures using corn meal. The grass in the pictures were in deep filtered shade of a large live oak tree. That was about as dense as it ever got in that area with zero hours of direct sunlight. St Augustine does not get thatch except under the most ridiculous maintenance practices. It would require daily watering and weekly fertilizing with a liquid spray. I have seen it, but only on one yard. And as soon as the management on that yard went back to normal the thatch disappeared. That lawn was growing entirely on top of the soil. Aerating won't help. Would you characterize your soil as sand or something else? Okay I just read back. This is Floratam? Floratam is the most disease resistant variety of St Aug. It is also the most sensitive to chemicals. Stop mowing it low and let it grow up for several weeks until it is higher than your mower's highest setting. Then mow every 2-3 weeks. The idea is to grow deeper roots which can get nutrition from deeper down in the soil/sand. You should see the new Floratam growing in at a faster rate than the disease can progress. You MIGHT still need corn meal to get rid of it, but tall Floratam in full sun can outrun a disease. Deeper rooted Floratam needs much less water and even less fertilizer. I have grown it up to 32 inches high in the Texas heat and drought, and it never needed either irrigation or fertilizer over a 2 year period. I'm not suggesting you do that, but the grass loves being tall. Here are some other tips to keep disease out of your lawn. Never put anything on the grass and leave it overnight. No toys, no yard clippings, no trash, no yard tools, nuthin that would cut off the airflow overnight. Disease will form in the morning dew if the dew cannot evaporate easily. Also be sure your soil drains well both downward and outward so it never puddles anywhere. You can improve downward percolation by spraying the entire yard with any clear shampoo at a rate of 3 ounces per 1,000 square feet and follow that up with 1/2 to 1 inch of irrigation or rain. And one last question: what is your watering regimen? How often and for how long do you water when it is not raining?