Is this separation anxiety since baby 2 came?

Every night my eldest used to wake up and I would pick her up and she would fall asleep on me automatically. So I probably did create some habit and she was used to me, not my partner. So when I went in for my C-section and I was away for five nights, my partner said that she didn't sleep very well and there was one night where she was screaming for two hours and he couldn't resettle her. I then come home with the baby and everyone told me she won't realize, she's really young, she'll be fine. I'm pretty sure she does realize. She isn't dumb, and I think it may have caused separation anxiety. We haven't figured out the room situation yet, so she sleeps in the cot and he is in the bassinet. Every single night she wakes up. Usually it's a little wake up for the dummy and she's fine, but it happens several times. Then there's been occasions where I thought she was having night terrors. She would be crying inconsolably for a couple of minutes with her eyes closed, and then other times she would just like wake up and cry and she would need me to hold her. So we started co-sleeping a few times. However, with my newborn, the way me and my partner would do it is he does the first feed, which is about midnight, and then I do the one that's around 3:30-4 a.m. When I do this feed, I'm always so stressed because I get worried my daughter will wake up. She often does, like 10 to 15 minutes in. It's almost like she senses that I am gone, and she'll start crying. So I have to run back into the room and hold her. It makes me really sad because I don't want her to feel jealous, but it's getting really hard with sleeping and waking up for both of them. Even if we separated rooms, it probably still happen. I guess what I'm trying to ask is, has anyone experienced something similar? Is this separation anxiety? And if so, how long is it going to last? Or do you have any tips?