I forgot to take the first pill in the new packet after having my period. Does that mean I'll need to use extra protection for a week or does it not matter seeing as it's the first pill?

Yes, you'll need extra protection until you've taken the pill perfectly (not missing any, no vomiting or severe diarrhea, no interfering substances) for seven consecutive days.

The first and last pill in a pack are the most important to not miss, since extending the placebo ("sugar pill") week to more then seven days means you're at risk for pregnancy.