Out of the blue

So I was talking to one of my acquaintances; it was very personal stuff that we are involved in, there were other strangers sitting in other tables in the room. We were just focusing on our topic until a woman who seemed to be of my granny's age; she poked her nose in out of the blue and caught my words and bombarded me with questions. I was somewhat embarrassed to realise that she was listening in on our conversation and felt uneasy about that, I tried to keep cool at that moment though.
After arriving home, I kept recalling her face and posture, tilting her head forward with full of nosiness. I got stuck in the memory of the scene. I know, it's not healthy to think of an event that gives me stress, but I can't seem to dispel the unpleasant feeling.

Really good work! Your written English is at a very high level, just be careful with your use of more complex phrases.