My Otos had a similar condition but not quite as bad when I came back from a longer trip. My tank had been taken care of by a friend – for which I'm very grateful! - but I think my friend heavily overfed the fish and the water quality plummeted badly. Besides the red mouth my otos also showed early signs of fin rot. I therefore guessed that the poor water quality had made my otos vulnerable to a bacterial infection which caused their symptoms.
What cleared the condition up pretty quickly was Melafix by API. The directions on the bottle state that Melafix should be added daily and a water change is to be made on the 7th day. That did not convince me since it didn't seem enough to manage the water quality issue. To make sure I talked to a friend who is a PHD chemist and pharmacist and he said that do to the chemical structure of the tee-tree-oil solution (that's what Melafix is) and the constant aeration of the water during filtration there is not much of a build-up effect to be expected over the course of a week. So it is not essential for the treatment to do only one water change at the end. As a result I did a 60% water change every day for a week. And added 0.5ml per gallon Melafix/API to the water daily. I also added in an extra airstone since the Melafix makes the breathing harder for the sick fish.
After 3 days I saw the first signs of improvement around their mouths and their breathing got much easier when I added the medication. And it got better and better from there. The fin rot also started to heal off at that time.
After the first week I felt that all the additional dirt and gunk had been flushed out of my tank and I returned to my normal water change and cleaning routine. I kept using the Melafix for a few more days until my fish looked healthy again. Actually I used it a few days longer after that. Just in case.
I hope that helped and you can get your otos back to health soon.
PS: I just remembered that traces of chlorine can irritate the gills of fish (if it is not strong enough to kill them). I have never seen it but I could imagine that it could look similar. Maybe it would be a good idea to check on the water conditioner or the possibility of contamination of the tank with tab water. Just a thought.
