The challenge is finding a doc who will prescribe it to you. I don't think many PCPs or Psychiatrists are going to just prescribe you valium right before a test. You will be hard-pressed to convince one to, although it seems that you have found one who will (I wouldn't guess that this is common though) And an urgent care place definitely will not. They won't prescribe you a benzo if they are not going to be able to closely follow-up with you.
As mentioned, the biggest impact of anxiety is in the inability to go to sleep the night before. Going to sleep the night before is what will make or break your performance (test, speech). If your anxiety prevents you from getting to sleep, you could fail a test due to inability to recall information; whereas if you had a fresh 7-8 hours of sleep, you might ace that same test.
The impact of anxiety on sleep is a snowball effect because you start thinking about the fact that you can't fall asleep and you keep looking at the time on the clock ticking away (many times you also keep having to go to the bathroom), and that the more time passes (and less sleep you get), you know the worse you'll do, which makes it even worse. It starts to become mental and makes it almost impossible to go to sleep.