Sink Smells like Rotten Eggs

A little backstory, we own a home built in the 50s, and when we moved in last year we had the sink and faucet replaced in our bathroom, as well as the plumbing. A little while after, we started noticing an occasional rotten egg smell, in addition to the sink backing up and taking about 30 seconds to drain. We called a plumber and they were able to clean out a massive amount of hair and grease from the sink, fixing the drainage problem.

However, now almost every time we turn on the faucet, the rotten egg smells starts. I’ve read a few places about the pesky overflow hole, and ours is at the back of the sink, right above the drain. Is there a way to tell if it’s the drain or the overflow?

I’ve already used enzyme cleaner overnight on the drain, and that helped for maybe a few days.

Any ideas?