I had a jury to my right hand as a child and started to use my left hand. All through school I was left handed. I went to Catholic school and the nuns never discouraged it.
The older I got the more I started to use my right hand again. I can write legibly with both hands and use my right hand for some things and the left for others.
My son is the same. He had an eye injury as a toddler and wore a patch for quite awhile. I think that had something to do with him being ambidextrous.
It’s possible. He was forced to rely on one side more than the other.
Being ambidextrous is a great skill. I’m glad you both have it.