Q.Cottonwood tree oozing
Is it sick?
Will it die?
Will it spread to the other trees?
Should I have it removed?
This could be a Canker disease or Bacterial Wetwood.
I've listed several articles to help you with your diagnosis.
You may want to have the tree inspected by a certified arborist.
https://www.colostate.edu/Dept/CoopExt/4dmg/Pests/Diseases/wetwood.htm
https://www.unce.unr.edu/publications/files/ho/2003/fs0333.pdf
https://www.gardeningknowhow.com/ornamental/trees/tgen/cankers-on-trees.htm
https://www.gardeningknowhow.com/plant-problems/disease/weeping-amber-in-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/what-is-bacterial-canker.htm