The problem isn't your rug. It is the fact that your current wall color has cool undertones and you want warm undertones. It is these cool undertones that make you feel as if the room is dark. Painting the walls with paint that has warm undertones will make the difference.

You can pick up paint chips from any store that sells paint, bring them home and tape them to the wall Use the same wall for all the chips. Be sure to leave space between each one. Look at them for a few days eliminating them as you go.

A warm beige would be nice with black wrought iron and would work with your existing rug. I see the warm beige color in the picture over the chair to the right of the fireplace.

The 'new' rug you are considering has cool tones as well and doesn't appear to compliment your furniture. Instead try a rug that has pops of color then choose one for the walls and another as an accent. See picture. This rug will also marry your fireplace to the rest of the room. Especially if you use a few touches of the brick red in accessories like throw pillows, candle sticks, flower pot or even books. It also has a heavier feel to better compliment your furniture.

If you paint the walls Do NOT leave the back of the built in this color. Warm and cool undertones do not compliment each other. The room would still feel 'wrong'. Instead paint the back of the built in the same color as the brick from the fireplace or in the green or blue from the rug. Then toss a variety of pillows in the three colors onto your furniture for a pulled together look.

Try rearranging your furniture to give your room a different feel as well.

Last, but not least, paint your mirror frame dark gray or black then hang it over the fireplace. hang the painting over the sofa and both will be shown off to better advantage!

Please post an updated picture when you are finished!