Did the sound stop when you lifted the arm off the turntable? If it did, or it reduced severely, then your problem is feedback. If it stayed the same volume, then your problem is hum. The arm won't shake visibly unless you have a relatively high compliance stylus or a relatively massive arm, but my experience with my various carts is that the arm shakes visibly. But then, I have relatiovely high compliance carts.
You can clean your RCA connectors with a spray on or brush on commercial cleanerlike Deoxit, or that spray
on contract cleaner that they sell at Radio Shack for 5 or 6 bucks a can, or you can get some 400 grit wet or dry sandpaper and just use that, or a Brillo or SOS pad to clean the RCA plugs and jacks. Just roll sandpaper into a fine tube, and put the tube into the center of the RCA Jacks, (KINKY!) and work it in and out. You must be careful in this operation, for your confessor will probably tell you that this sort of activity is a near occasion of sin. You can use the 400 grit on the pin and inside the ring on male plug, and on the outside sleeve of RCA jack. Just sand enough to take the crud off. Don't go crazy, a little is a lot.
And good luck from the old sinner, living among the near occasions, and fighting them off,