It sounds to me like there the drain is not sloped enough. A drain needs to be sloped by at least 1" per 4 feet of length, and while more is OK, it should definitely not have dips with high spots. It's pretty basic that water will not flow up hill under gravity. Years ago, my father had a home with a basement drain under the slab that did not have enough slope. It required clearing about once a year due to accumulation of debris. Proper repair would have required very costly concrete removal to redo the slope. Realize that (a) this needs to be professionally done, and (b) professionals do not come at bargain basement prices, this will cost you some $$. To state what should be obvious, this is NOT a DIY job, especially for a novice. The plumber that raised the sink improved the slope away from the sink, but did not go nearly far enough. You've already had this advice from the plumbers, there's no magic fix-in-a-can for $19.95 plus shipping that will make this go away, nor is there any secret trick that will remedy the problem. I'm sure you were hoping for advice that would tell you how to DIY this for cheap, but sometimes, you just have to bite the bullet and pay the man.