I am sorry you had to go through this. Hopefully, your other ovary will "pick up the slack." But it is possible that you will have reduced fertility and/or early menopause. I think it is important for you to know this so that you can get proper intervention if either occurs...hoping neither does.
The chances of it happening again is minimal. I would not worry about it. You can adjust to one Ovary. Losing one should be okay. I had to lose both to Cancer and I have adjusted. My life was on the line. You have to do what you have to do. You really had no choice. In a perfect world women would keep there ovaries but things happen. You might even feel sad because it is a part of us thats normal.
Alex