Beautiful bloom. Looks like Buds Pink Cloud... Sorry you had damage.... Your original plant should be fine... maybe you could post a picture of it. Where the break was on the original plant how far up from the base was it? Depending what you have there I would suggest cutting it again so not to be jagged but I would really need to see it. The stick you have in water... I would go ahead and cut off the leaves and blooms
and let the cutting dry. If you have a "Y" you have two tips, a choice stick to root and plant! One thing I have learned over the last few years is plumerias really don't like fertilizer that much. If you over fertilize they can get long and lanky and that makes them more susceptible to breaking and outgrowing the root support and can lay over... so be careful not to over feed. Over feed and over water are 2 no nos in plumeria care.
There is a book out by Jim Little called Growing Plumerias in Hawai'i and Around the World. It is WONDERFUL. I suggest it to anyone who wants to learn more about Plumeria care. Has detailed instructions on rooting, grafting and care of plumeria. You can get on Ebay or from Amazon. I ordered mine from Jim Little Farms when I got a cutting from there. Plus the pictures of the blooms are awesome!!
Good luck and I hope this helped ....
RobertB
Bud's Pink Bloom