You don't want a cotton-seed producing Cotton Wood tree in your yard because of the damage they do to air conditioner units and filter systems. So I recommend you take cuttings from your tree and root them.
Here's what Google says.
Cuttings from cottonwood and willow trees are able to sprout roots and leaves easy. Small cuttings of new growth, called whips, or larger cuttings from older wood, called poles, can be planted in the soil. Once planted, these cuttings can quickly turn into trees.