Taking the pill before your period?

I got the pill prescribed last Wednesday.

My gynecologist told me that I should definitely wait until I get my period before taking it (I have a very irregular cycle, currently it's 60 days).

On Monday, I started having brown discharge, and on Tuesday, I had a little blood, but I usually have very heavy periods, so I thought I should wait a little longer. I started taking the pill on Wednesday evening. Today is Friday, and I'm still only having very light periods, if any at all.

Was it okay to start taking the pill on Wednesday?

Can there be any side effects?