What kind of grass is this?
From your seed head description it may be green kyllinga,see the attached link.http://turfid.ncsu.edu/csPagedPdField.aspx?PlantID=KYLSS
Green kyllinga is a perennial sedge often found in damp wet areas.http://oak.ppws.vt.edu/~flessner/weedguide/kylbr.htm
We do not have research on the specific herbicides and their control. The product by Ortho Nutsedge Killer, active ingredient Sulfentrazone is one of the herbicides that offers suppression/control and this is a post emergent. You will have to follow the label directions. More than one application of an herbicide may be needed and control may not be achieved in one season.
You will most likely see this sedge through September so you can apply now if the turf is not stressed. It is best to control when the weeds are small and actively growing next season. This is a weed that is difficult to control and will require persistence on your part.
If your lawn is more than 50% weeds, it needs to be renovated, i.e. totally killed and reseeded. Throwing herbicides and fertilizer at a lawn that is 50% weeds wastes time and money, because the grass cannot grow fast enough to fill in the blank spaces left when you kill weeds.
You may want to get a soil test to see if the pH and nutrient levels are correct in your lawn. Then reseed. Late summer/early fall is the prime time to seed lawns.