Green, purple, blue or yellow - they're all examples of CAs particularly in digital imagery. All such colors and hues can be removed by essentially similar action in post processing. Fringing occurs when the colors of the light wave aren't all hitting the image sensor at a 90 degree angle (essentially it is a lens induced problem, as the light travels through the lens optics, each color is not equally treated). The different colors of fringing occur due to the individual light (color) frequencies, and "shift" accordingly. Commonly referred to as purple fringing, most prevalent, since purple is the furthest color from the sensor and depending on the f-stop can defocus.
If you are find fringing on one side of an image, check the other side automatically. And again after you have corrected the purple side. Green is the complementary color to purple, so when you have a chromatic aberration the color that shifts on one side will logically end up with a complementary color shifting (or bleeding) on the other.
Sometimes the post processing CA capability can't help you without introducing other/additional problems - for instance, if you have blue on one side, but not matching yellow on the other side, then sometimes fixing the blue can create a yellow fringe on the other... or if not, it may put a line around the edge on the opposite side, somewhat like what you see with over-sharpening. If you have that problem, then often you can fix it by creating a new layer on top of the original layer and changing the blend mode to "color" - then select the color next to the object that has the fringing with the eye dropper tool, then a soft brush and color over it - the fringe should disappear. This, however, like any other fix, may introduce extra problems so you have to be careful. It can be a game of wack-a-mole.
Most post processing utilities/packages have the capabilities to correct CA. Check the manual or search on line for instructions for the particular utility you are using. Sorry, I didn't read the last line of your post. PhotoShop (but its very expense), LightRoom, really any of the packages. Most of these packages offer something like a free 10 - 30 day trial, so that you can see how it performs and if their workflow appeals to you. I would first start out with something like LightRoom, or Corel Aftershot.