Who goes first?

Your at a stop sign with your turn signal on to go left. You have to wait for traffic to pass on both sides before turning onto the road/intersection. Across this road is another stop sign, another vehicle approaches from the opposite side while your waiting to turn and they have no blinker on, so they intend to go straight. Who goes first?

I’m not sure if this classifies as controversial, but I decided to ask anyway. 😬 This situation happened to me yesterday, I tried to turn onto the road and the other vehicle came across and almost hit me. I had to slam on my breaks and stay sitting in the middle of this busy road while they continued to cross. I thought I was suppose to go first since I was at the stop sign first... but maybe I was wrong 🤷🏻‍♀️ It scared the shit out of me, and my son was in the car with me. And then this lady had the audacity to flip me off... was I wrong to think I go first?