#Mathematica, 63 94 103 bytes
When I first saw this challenge, I thought Sweet! Mathematica would be perfect for this! until I noticed that built-ins were banned :'(
But wait! I can use bar graphs!
r=RGBColor;BarChart[{1,1,1},ChartStyle->{r@"#0055a4",White,r@"#ef4135"},BarSpacing->0,AspectRatio->2/3]
(Thanks to Martin Büttner for shaving off 5 bytes but adding 16)
Looks like this:
If you add ,Axes->None it looks like this:
If you don't care about the border, you can use this: (95 bytes)
r=RGBColor;BarChart[{1,1},ChartStyle->{r@"#0055a4",r@"#ef4135"},BarSpacing->1,AspectRatio->2/3,Axes->None]
Looks like this:
Without axes:
