You are experiencing acoustic feedback. There are two types, structure borne, which enters through the rack, or stand, and is transmitted through the TT suspension, and airborne, in which sound waves directly excite the plinth of the turntable.
Since you have already made a very smart move and gone to the wall shelf it might be best to try to determine if the remaining issue is structure borne or airborne.
You might try removing the record player from the wall shelf and placing a glass of water on the shelf. Play another source, CD or streaming, whatever you have, and observe the water for movement. Heavy movement will likely indicate structural issues, in which case a TT with a different plinth may help as well as putting a bicycle inner tube under the turntable. It is also possible that a high-pass filter will help, such as the one marketed by KAB. For me that is a last resort as this does have an effect on phase response in the audible range, and adds a set of interconnects, but in some instances it is a perfect cure that eliminates the problem.
If it is airborne, then you have to look at moving the turntable to a place that will excite it less. Play a CD with heavy bass and move your head where you might site the turntable. You will hear areas of greater and lesser bass accentuation. See if you can move the turntable to a place that has less bass accentuation. That will often help.
I hope that helps a bit.
