Grease clogs can be cleared by using an enzyme drain cleaner to safely open the drain. Use it at night when the drain will not be used for several hours, and do it three to five nights in a row. Once the drain is open, using the enzyme drain cleaner a couple of times a year should keep everything running smoothly.
People think the hotter the water the farther down the drain the grease will go. Actually, when grease is rinsed down a drain with cold water it coagulates into a solid and bounces down the drain. If chased with enough water it should make it to the main sewer and out of harms way.
Now when hot liquefied grease is rinsed down a drain, it is like a coating of hot tar. It applies a thin layer over all the existing waste in the drain bonding it together. Do this over and over and soon the drain is completely clogged and sometimes even a sewer snake will not open the line. My pal Jim, the retired sewer man, likens the clog to sending a snake through a bowl of Jell-O. It will go down the pipe and come back but the grease and the clog will not be moved.
To unsafely open the drain, try pouring boiling hot water down it. You will have to bail out the sink first because it won’t work through standing water. This might get you through the evening. This should be done by a competent adult due to the possibility of scalding from the hot water.