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We would not recommend rooting hormone.
This article will help you.

https://www.gardeningknowhow.com/houseplants/lucky-bamboo/lucky-bamboo-rotting.htm

If you can include a picture of the plant, then it will help me to see what is going on. It looks like the wrong photo may have gotten uploaded.

Although these are called "bamboo" they are actually a species of Dracaena! With this being said, they have a different care than bamboo will.

They are very well adapted to being cramped up in a small container, and prefer to be cramped, but should you feel that you need to transplant, then you will want to choose a well draining soil and transplant as you would any plant.

Take the old plant out of the container, and hold it up to the top of the new container so that you can see how much soil that you need to put under it. After you fill the soil to where you need, then place the plant on the soil and fill in the sides up to match the level of the old containers shape. water in and let ALL extra water leave the container through the drainage holes. Add extra soil if needed. Some will compact down after watering.

This article will give you more information on the care of these: https://www.gardeningknowhow.com/houseplants/dracaena/dracaena-houseplant-care.htm

The leaf that you show is from a completely different plant variety; it is a Philodendron brandtianum and could not have grown from your Lucky Bamboo.
Perhaps your friend was growing a few of these cuttings in with your Lucky Bamboo.

Gotta love bonus plants!

Since these are actually a type of Dracaena and not a true Bamboo, you can prune these to fix their shape! They have a different growth habit so pruning can help them to be more "full" looking.

This article will help: https://www.gardeningknowhow.com/houseplants/lucky-bamboo/pruning-lucky-bamboo-plants.htm