Bathroom sink with bad smell

[Qualls6]

Have dual sink vanity. One side has rotten egg smell when you first turn on water. Doesn't matter if it is hot or cold. I replaced drain and p-trap. P-trap is level. Isn't hot water heater issue as it only effects this sink. Thought there might be some back pressure pulling water out of p-trap so I put cellophane over drain to see. No movement. Repeated treatments with drain cleaner with enzymes. Nothing works.

Suggestions?

 

[KULTULZ]

Both P-Traps are vented properly?

 

[Qualls6]

How do I know if vented properly? I didn't think of overflow being the issue. That makes perfect sense.