I agree with Brandi re BM White Dove. Agreeably you want a cream white vs a bright white to compliment the existing muted golds in the upholstery and area rug. Otherwise this cozy rather rustic room is to tip into a more modern room. But maybe this is what you wish?

Painting your bookcases is HUGE! Really think it through. These architectural details are fabulous focal points!

TIP: Remember the back panels of the bookcases can be painted a complimentary or contrasting color too! This way your eye flows from bookcase to bookcase.

Consider the following suggestions to break your box:

1. Pull one of the accent colors from upholstery or area rug and place in areas behind bookcases and on the bricks ( for example the muted green or muted red), creating fluidity.

OR

2. Select a color that compliments muted green, red and gold? Hmm. What color could this be? Are you sitting? You really need to be sitting. :)

A muted plum (example SW Expressive Plum or Mature Grape) OMG! Not what you were expecting? I know. Are you writhing, lol or thinking hmm what if?

In design you must explore all the "what ifs"?

3. Or pull out the stops and paint the background of the bookcases a muted gold, or do an up- do, yes I said up-do and paint with a metallic gold to add ZING!! Or take that raspberry red across.

AND NOW The Grand Finale of Suggestions...

4. OR.... Paint the bookcases your raspberry RED or whatever that red color in the carpet is! In an eggshell finish. AND the brick a muted GOLD! Forget the white or off white (snooze) and go bold! Just imagine!

RE the TV above the mantel? So sorry... Never been a fan, because its unnatural to be looking up so high at a screen. If you are adamant, then consider the TV hidden in artwork. You can Google this.

At the very least you wont be looking at two black holes on this wall area all the time. (As The TV would be one and the fireplace opening/ fireplace screen the other). Unless...

RE the Fireplace Screen. Pretty, but she needs a little oomph. But you can decide exactly what after the rest of your decisions! I cant tell you everything.
Are you good for now? I need a nap.

Explore, take your time, have fun!

Cheers!

Andrew