I wouldn't claim to have saved a life. I think that guy could have gotten free on his own. I'm glad I helped him but wouldn't want to overstate my contribution.
You need a way to help people float and to pull them in.
Do not let a drowning person grab you they may kill you.
If I had stopped to think I would have tied our two dog leads together and thrown them in. I could have pulled them in quickly. They were only 3 or 4 meters from the shore.
Another option would have been to link arms with the strangers there and pull them out together.
An incredibly sad story I heard a few years back, when a dog could not get out of the water and seemed to have started drowning, so a boy jumped in to help the dog but then also started drowning, and so his father went in trying to rescue him. Both drowned; the dog somehow managed to get out of the water on its own…
I just want to echo the advice: talk to someone, preferably a professional. You've been through the wringer. Best wishes from the other side of our planet.