Near miss- driving

Hi all,

This evening I was at a four way set of lights, when it was my turn to go.
A person waiting to turn onto the other side of the road whilst I was waiting to turn on his side allowed me a gap to turn.
I edged forward into the gap but didn’t go far as I couldn’t see past him and the traffic the other side of him.
A car the other side of him slammed on his breaks and came to a stop.
We both looked at each other when I held my hand up to say ‘sorry’ from inside my car.
I believe this person then continued to carry on driving forward and carried on as normal. I continued to make my turn as it was clear after this.

My question is, I’m terrified. Have I done something wrong? Should I have gotten out and spoken to them? We were in a busy junction..

I’m so worried and concerned I’ve done something wrong. I’ve never had anything not even a parking ticket in the 10 years I’ve been driving. It’s making me question whether the light was even green for me to go😖