Facebook Alerts For Certain Posts?

If you are talking about Facebook there is option to mute notification coming from any post.

Probably not. However, you can set a Google alert which may or may not help as a person's individual Facebook privacy preferences will dictate whether a post will come up on Google at all. Furthermore, it's highly likely you will not be able to get responses to posts, e. g. Member1 says "I'm looking for a doctor in Salt Lake City." and then Member2 replies, "I'm looking for a doctor in Dallas." Of course you want Member2's info.

But it is HIGHLY unlikely Facebook will make this available as they really just want to sell you advertising. However, FB ads at least are pretty cheap. So consider placing an ad and targeting it with laser-like accuracy at just people in Dallas. Let's say if you're a gerontologist then you also want to limit by age, say, 60 and above. If you're an OB-GYN then you also want to limit by gender. You get the idea.

But Facebook is in the business of selling advertising, and the users are the product. Setting up this sort of alert would be (perhaps) fairly easy programming, but it would strain their system, as it would potentially require a query on every single account (there are something like 1.8 billion of them these days and, yes, that's billion with a B) every minute of every day. This query would potentially crash their system. Plus they would lose out on ad revenue.