I do energy consulting, and it's hard to effectively shade east and west windows from morning and evening sun. Awnings on the west lose effectiveness because the sun gets lower and lower in the sky as it sets, requiring an awning to be lower (blocking the view) to still provide shade to the window. An awning will help to block the more southern portion coming around earlier in the day, but the most effective would likely be adjustable exterior blinds or coverings rather than an awning.

As you've discovered, interior blinds aren't very effective too. Once that sun is through the window, it's hard to get back out.