clogged kitchen sink help

[sixto]

Our kitchen sink is very slow to drain. It happened all of a sudden. One moment it drained properly, the next moment running the garbage disposal sent effluent into the adjoining bowl. After sitting overnight, 2-3 gallons will go down the drain before it backs up into the bowls. Two treatments of Drano MaxGel didn't help.

The sink has two bowls with the disposer teeing into a vertical pipe with the p-trap. There is an access port on the exterior wall about 3 feet from the p-trap at about the same level.

Should I send an auger through the p-trap or the exterior access port?

Thanks,
Sixto