new cat attacking resident :(

i’m kind of at a loss here and i’m thinking it might be time for medication. my resident cat (5F) is just consistently getting targeted by my new cat (~3F). I adopted the new cat in the beginning of october. she was an abandoned stray estimated to be three years. my resident had never been around other cats before but she’s a sweet angel so i thought i could make it work. i did the whole jackson galaxy introduction and took things very slow. my resident ended up with a uti that progressed into a kidney infection so i have had a divider in my house and they do not have access to each other at all. i have feliway, extra litter boxes, multiple water dishes throughout the house, done the under the door with the food introductions, tried to do play/treat time through a see through gate, sight swapping, you name it. i live on my own so i have had accidental interactions and my new cat just chases my resident cat down. at first i thought it was just her trying to play, there didn’t seem to be any aggression behind it, but these incidents have happened multiple times where my new cat has literally outsmarted my separation moves to seek my resident out to attack her. i obviously don’t know this for sure, but the only thing the new cat is lacking in access to is me, and i am beginning to wonder if she is getting territorial over me and not just her space. regardless, i don’t know what steps to take next. i am tired of having to keep starting over. i dont want to stress my resident cat out to the point of her getting sick again. i dont want to have to rehome this cat and basically abandon her like she already has been. she is so so sweet to me. but she just broke in to my bedroom at 4 am and attacked my resident and it makes me sad thinking that she is so stressed by this other cat that she has to get crazy to break into my bedroom to attack a cat she couldn’t even see. i’d obviously like to talk to a behaviorist but the ones who come to your house are ridiculously expensive. i truly think the plugins are not helping enough. is it time to consider rehoming? is medication for anxiety too invasive? any advice on what steps to take would be very appreciated.