Ok, your convinced it is the drain, lets deal with that and verify that first. If it is the drain the noise would occur when the water is flowing down the drain. Plug the sink fill it with water if you hear noise while it is filling but plugged it is the supply lines. Next turn the water off wait a few seconds and then drain it. If the noise now occurs and did not before it is the drain. Please do this with the shower as well and let us know for sure which it is. If you have already performed these task in the past I apologize for being redundant.