Even if you don't want to do it, take the faceplate off, shine a light inside, and check to see if you see a bare copper wire in the back. Being able to give that information to an electrician might change it from "I'll call you in 8 weeks when I have a chance to come give you a quote" to 'Well, that's a quick job, if the end of the day works, I can run by after my Thursday job and take care of that real quick.
When I sold my old house, I had outlets on both sides of my kitchen sink. The one to the right was on the same circuit and closer to the box and was a gfci, so it was protecting the one on the right as well. Which could be confirmed with similar testing tool as posted above designed to trip the gfci. Their inspector claimed both had to be gfci outlets. I honestly don't if that's the case based on local codes, but a 20 dollar outlet wasn't worth fussing about. I then learned I had to have a licensed contractor make the change. A little annoying. I had no luck finding an electrician that could come out quickly even for that, ended up searching 'handyman' and found a local jack of all trades guy that was licensed and came out within a day or two.