I had my sons cat, then he took him back home and I got my own. About 5 months later he had to leave town, and we took his cat in again, and we had this exact problem. It is a territorial thing.
It took ours about 3 or 4 months before they would exist in the same room with one another. Sometimes putting the newcommer into a kitty crate and leaving them in a room together helps./ That way they cannot hurt one another but still get to know each other.
Try not to favor either one, for jealousy is a big problem. For some reason my older boy cat hissed and growled a lot, and when I scolded him he did it more, but if i pet him and told him he was a good cat, he stopped immediately.
I would not worry too much, but if things do get rough and they fight, sometimes a squirter bottle with water in it will stop that but dont do it very much. Dont feed them close together, but in time move their dishes closer a bit each day.; You cannot force them to be friends but usually the younger cat will pursue the friendship. Cats make a lot of noise getting aquainted, so dont let the hissing and growling bug you too much. Sounds like the first cat just needs to be reassured and give her time.