Red gills usually means high ammonia, is he flaring a lot? Does he seem to be struggling to breath? When was your last water change? If I remember correctly you've been doing a lot water changes so the water parameters should be safe. Can you get a pic of him, I'm not sure about the white around the eyes. Are you sure it's not just the way the light is hitting him? Does the white appear to be on the eye or on the outer part? Is it fuzzy?
The red color is generally a sign of oxygen in the blood and good circulation...The gills should look red..when they look off color, pale, purple and they are gasping, have rapid breathing, sometime yawning a lot, may or may not have clamped fins, lethargic to name some common S/S of ammonia and/or high nitrite problems...then you need to intervene.....
I can't get a good picture of him, ook about 50 shots but all show nothing.
He's not flaring a lot, only did it when he saw Pudge.
And he doesn't gasp, just is his normal self. The red only comes when he's flaring, but foes away seconds later
And there's definitely a thin white ring but its not powdery or puffy
If he's only flaring on sight of the other fish & not gasping I wouldn't worry too much. But I would suggest doing something about the two of them being able to see each other. Some Bettas can be too stressed from seeing another one all of the time & can end up having ill effects.
And as oldfishlady stated, the red can mean healthy gills as well, I should have thought of that. I focused on your stating it looked like blood, my appologies.
The white around the eye or eyes is hard to suggest without seeing it. One of my females seemed to have something wrong with her eyes a couple of weeks ago, they seemed to be going white, not cloudy, but not normal. After a week they're back to their normal black, it was very odd.
And Buddhas tank was moved in front of Pushes for the few minutes it took me to get pictures. Where he is noe, there wasn't much light so I had to put him by Pudge so I could get pictures. Their.tanks are a few inches apart from each other with two of the mesh sheets between them. A bamboo cup is also between them :)
I did some quick research and someone said it.could either be aging, or just a color change in the fish, and to be worried if the eye grew...