What species of Gourami are you all referring to?
I have only kept Trichogaster trichopterus
I have a female that has a broken blood vessel on the tip of her Dorsal that created a red spot. (see thumbnail)
As for the redness around the gill, I would keep an eye on it.
Could be bacterial infection. Especially with the symptom of laying low.
As for the chasing, He is just claiming his territory. If the
aquascape permits him to have his own territory, and there is plenty of room for other fish. Then it's not a problem. I have found that 2-3 females per male makes for the best temperament.