Side to side is a serious problem. Maybe even more than front to back. The thrust washers keep it from moving front to back. Side to side is something else entirely. I don't even know if bearings can wear that much to give you detectable side to side movement.

The bottom line here is any crankshaft movement is bad. Anything you can feel with your hands is way beyond stock.

The next bottom line is that you need to diagnose this. We can sit around all day speculating about the problem and giving you ideas, but...you need to get a hard diagnosis or just replace the engine and figure out what the failure was at a later date. We are not there, we cannot see it. Driving it is a bad idea. It needs to be fixed and we are at that point where you or your mechanic need to decide the next step.

Good Luck,
Michael