Kitchen Sink Clogged Please Help

My kitchen sink started to clogged up a few days ago and I used the plunger and for some reason it gotten worse. The I remove the trap under neat the sink and it was clear but the drain was still clogged up. I then remove the horizontal pipe that is connected from the trap to the wall and used a auger (snake) and I was able to push the snake all the way down the pipe (15' snake). Did this a few time and re-install all the pipe, flush it with boil water and the the drain backup again. Pleae let me know what I can do next to clear this clog.

Thanks,

You need a longer snake. You can buy one in the hopes it is long enough or call a plumber. 1 thing you may not know is if the snake is going up the vent instead of down the drain. If that is the case the snake you have is long enough but to flexable or you just need a power auger.

If you call a plumber the problem will go away quickly.