Is it fin rot?

[Sschwenk]

Hello, this past Sunday I picked a lavender gourami from my local fish shop. He showed no signs of illness at all when I picked him up. As soon as I put him in the tank he was extremely skittish and wary of me, understandably. He looked healthy until I woke up this morning and found a black patch on his tail. He seems ok otherwise, however I can’t get a great look at him because he is still shy. My water is good, with ammonia 0, nitrite 0 and nitrate 10-20ppm. My guess is that stress weakened his immune system, making him susceptible to any bacteria lurking around. It concerns me that a patch this large appeared so rapidly and makes me wonder if I should medicate immediately ( If it is indeed fin rot) or just perform another water change and let it heal. Any advice would be appreciated. Attached is a horrible picture, but you can still can see the black patch. Unfortunately I can’t get him to come any closer for a better picture.