Need a second opinion

Our shower has what I think is pretty obviously mold. Small black dots that consistently appear on the tile and in the grout between the tiles. My wife is convinced this is just mildew. Whenever it appears, she gives the shower a good scrub and usually gets rid of the stuff in the grout pretty easily but the black dots on the tile tend to be much more difficult to deal with, and often remain.

The wall on the other side of where the shower head is has previous water damage. We thought the source of the water/moisture had been removed but recently, the area appeared darker than it usually is, so I felt it and it was moist. Evidently, the source of the water/moisture has not been removed. About 2 days after this happened, the shower had more black spots on it than it has ever had.

Is it presumptuous for me to think this is most likely mold? I’ve read that DIY kits that you send into a lab are typically unreliable, but is that primarily the case with air sampling? If I’m able to physically scrape some of the “mold” out of the grout and send that to the lab, would the results be any more reliable than if I were to do air sampling?