I'm not a plunber either, but if the U bend is clear it suggests the blockage is further down the system. Does anything else drain into the pipe, e.g a dishwasher, a d if so, is that also affected?
We had a similar problem. The pipe beyond the u tube to the drain is about 4 metres long. We had a lot of trouble with it, and eventually a plumber told me the wrong diameter pipe had been fitted Apparently beyond a certain length the diameter has to be increased to compensate for the slower flow through the pipe. Having it replaced would have been costly, so we coped with it for years. Eventually it completely blocked and the flow reduced to little more than a slow seep. In some desperation i used seversl bottles of drain acid, one after the other. As each seeped through i opened the next, until the pipework would have been full of the stuff. It suddenly cleared and we have not been bothered since. I suspect a fat plug had built up somewhere along the pipe and the concentration of acid finally loosened it the point where it flushed away. If you try this be very careful. The acid is VERY dangerous. Use goggles and thick rubber gloves if you have them. If you get any on your skin wash it off immediately in running water and seek urgent medical help. If you get any on your clothes remove them quickly before it can soak through to your skin. Pour it very slowly and gently and keep everyone else out of the way. I was never splashed, but the stainless steel sink is now permanently stained, which gives an inkling of how corrosive the acid is.
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