Probably not. Color filters can be useful when you want to get a certain look in a black and white photograph, but usually don't enhance color. That's because they are inherently restrictive — they subtract colors from the scene.

Probably what you need is a) better lighting on the painting and b) to shoot in Raw so you can make careful adjustments to bring out those subtle differences in reds.

It's a good idea to color-calibrate your monitor, and the suggestion of working with a color target for accurate color isn't a bad one. And, definitely do not use automatic white balance — set it manually to the color of your light source, or use a gray card.

I should also mention that a filter can help with one thing: if your paintings are reflective (oil paints, say), using a polarizing filter on your light source and on the camera may be helpful. There's a good tutorial on that at http://chsopensource.org/2013/02/27/polarized-light-photography-for-art-documentation/. but from your description, this isn't the issue you are dealing with.