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The Weed & Feed treatment last month probably used fertilizer with Atrazine as the herbicide. Scott's Bonus S is an example of such a product.
After examining your photo, it appears that the weeds that Atrazine targets are nearly gone, but you have grassy weeds that need to go.
IMAGE Nutsedge Killer is safe for use in your St. Augustine lawn, as well as Bermuda, Zoysia, Centipede and Buffalo grass lawns. IMAGE will kill cool season grass like fescue and rye, and grassy weeds like poa-annua as well as many broadleaved weeds, like clover, dandelion, spurge and henbit.
Apply IMAGE to the soil and allow it to dry for 24 hours. Within seven days after that, the area needs to receive enough rain to wash the product into the root zone of the weeds.
St. Augustine does not require much in the way of fertilizer, so feed it twice a year (Spring and Fall) and use these specialized herbicides sparingly, when the temperatures are below 85 degrees.
Eliminating the weeds will allow your lawn to fill in where the weeds were after the temperatures heat up in the summer.
Shady areas will not support St. Augustine grass, so you might consider shade tolerant fescue grass in those areas. Plant fescue in the fall. Keep in mind that IMAGE is not safe to spray on fescue.
Keep us posted with your progress!