Sorry to hear this, it sounds very hard for you. First and foremost I would stop bringing her out of her room. Whether its to go downstairs to watch telly, your room or anywhere else, it's not a good idea to remove her from the room as this sends the message she can wake and no longer has to sleep. She'll quickly start to expect to be taken downstairs and it will make things harder for you in terms of resettling her.
Not sure what to suggest sadly if you have tried all of the above methods you mentioned to resettle her... how is her speech ? Have you tried asking her why she feels like this ? What the problem is ? Let her speak without putting words in her mouth by asking open ended questions like 'why are you screaming ?' in a neutral loving voice. I know this may sounds silly but you never know what she might say, you can then help her to over come the problem.
Also, perhaps it's worth choosing a method to resettle her and sticking to it and stop trying various methods as she needs consistently. So pick what works best and stop changing method - for example, keeping her in her bed but staying close to her until she calms down then leaving the room. If she cries again, then you come back and start over again until she resettles. It would definitely be exhausting for you to do this in the middle of the night certainly with a new baby but worth it in the end.
Or have you tried talking about what happened with her the morning after ? Speaking to her about it over breakfast and explaining why sleep is important could help ? Everything is harder at night. Explain that when she cries and screams at night you will come to her room to help her but she won't be coming downstairs anymore. Choose how you will resettle her (i.e staying in her room by her side until she calms down) so she know what to expect. It might take you several times to resettle her but perhaps when you are trying various methods she's sensing a lack of confidence and leadership from you which is why she continues to cry and things escalate. Be confident in your choice and stick to it. Could take a few nights before seeing improvements but if you are confident, consistent and calm in how you handle the situation during the night this might just help. You may already be doing this and in this case I don't know what to suggest... sorry.
In the past when my toddler has struggled to resettle we've allowed her a little toy or book to look at/play with in bed. She's never allowed out of the room nor out of bed but giving her something to look at like a book whilst staying in her bed has helped to calm her down. She then dozes off eventually.
If you don't find a solution just remember like everything this will pass quickly but be careful not to fall into bad habits. Taking her downstairs to watch telly will soon work as a reward (like it would for most kids) so then she might start to think if I cry my parents will give in and I can watch telly. Obviously she's not consciously thinking this at her age but toddlers aren't silly and even the sweetest of them still know how to get what they want.