It's pretty easy to test if the cartridge is failing. Change the connections at the cartridge while leaving the turntable rca's plugged into their current location. With the phono preamp turned off, of course, swap the red and white leads and then swap the blue and green leads. This swaps the left and right channel of the cartridge.
If the same speaker has sound as before the swap, then the cartridge is OK and the fault lies with the tonearm cabling. If the sound now comes from the other speaker, then the cartridge is the culprit.
If it is the cartridge, you won't be able to fix it with a new stylus, you will need a whole new cartridge.