Getting sick during the seven pill free days has absolutely no bearing on the pill's efficiency. So long as she took the 21 hormone pills correctly, then you have nothing to worry about.
Your girlfriend is EQUALLY protected the entire month. She is no more at risk during her pill free week then at any other time during the month, so long as she takes her pills correctly: every day and on time. The pill, when taking correctly, is 99.7-99.9% effective. The fact you are using condoms in addition to the pill means the odds of her getting pregnant are even smaller.
Relax, you're fine.