Have you balanced the arm, set the tracking force scale slip ring to 0, and then turned the counterweight until the scale now reads 2.5 grams or so? You might simply be tracking at too low a tracking force, either because the arm wasn't balanced and the scale zeroed properly, or because you have the common impression that lighter force is gentler on records - it's not. The needle needs to stay in firm contact with the groove so that it doesn't start crashing around from side to side. In your case, feedback, not just mistracking is happening, so it's a worst case scenario.
Vinyl is pretty resilient, and apparently the pressure and frictional heat as the stylus passes over it liquifies it momentarily, and it essentially bounces back as it cools. But being smashed with an errant stylus is going to gouge and dent the groove, and it can't bounce back from such damage. So, outside of laboratory conditions, it's safer to use a tracking force in the upper half of the manufacturer's recommended range.
Obviously different cartridges and different stylus shapes require different tracking forces to be at their best, so my recommendation is not to just jack up the tracking force to 11 (which is one more than 10), but to start with something nearer the top than the bottom of the recommended range. Then you can fiddle around and see what you can get away with.
Obviously all the recommendations about getting the suspension tuned up are good, but I think your problem may be simpler than that. If, after checking the tracking force, you still have problems, check to make sure that the top plate lock down screws have been loosened - if the top plate is screwed down to the base, you have no suspension.