I trust this is sufficient?
First, add a Dodge & Burn layer. Don't do anything with it yet.
Above that, add a Channel Mixer layer:
Red +100, 0, 0, 0
Green +75, 0, 0, +8
Blue +65, 0, 0, +6
Mask it carefully to the sclera. It'll take care of most of the red, but will leave some slight dark rings. So to deal with those, use the D&B layer. Work with a 5% brush.
I hope you'll take the Channel Mixer class before too long. It's so handy for so many purposes.