there are many ways to arrive at a reasonable color balance - i may add mine later (between meetings), however for reducing the air-glow effect, since green and aqua are not present in great quantity in the rest of the star field, you could start by lowering the saturation of the individual color channels for green and cyan.
Sometimes the horizon is also overly bright due to light pollution from nearby cities - there is a pixel averaging technique that can help to bring that down a bit as well using a simple digital grad and masking the foreground.
At first glance, this image seems too red and green overall and does not look natural to me. While the true colors of space may reside more toward the warm side than the cooler blues very often seen online, I remind myself that I am interpreting a scene artistically and not necessarily documenting exact light wavelengths for NASA, so I will occasionally render my star field more blue, green, yellow, etc to complement my foreground if applicable.
I have never introduced colors to my milky way shot, but will spend a good bit of time shifting the relative color bias to find where the best mix of individual colors are revealed, which I find lends to a pleasing result (YMMV).
some samples:
https://www.flickr.com/photos/mikeoria/albums/72157649944280914
pm me if you want some hints on doing this - happy to help.
gotta run!