Two issues. 1stly the separation anxiety: I thnk you're just going to have accept this one. You can't change the situation, it's a normal develomental stage. I found a playpen very useful. the baby could see me and be with me, but didn't have to be held all the time. It worksbetter with some dc than others - some are more independant, some are clingons.
As for the 2nd issue, the settling to sleep, I think youare going yo have to bite the bullet and accept that there is ging to b some crying. I'm not saying to do CC. But if you consistently to the same thing, and be boring about it, she will eventually accept the new status quo and go to sleep more easily. It could take a week or itcould take a few months. But you have a few months. So it's not a crisis right now.
Set up a bedtime routine that you can repeat very accurately. Always read the same little book (or, to save your sanity, one of no more than three). Then cuddle her in the same way, tell her the same "dd is sleepy and is going to fall asleep in bed now " settling down phrases. These phrases are as much for your benefit as for hers, because you are telling yourself it is going to work, but eventually she will recognise them as sleep cues. (I've been telling my 3yo the same settling down phrases since hewasyour dd's age, and, no matter how bouncy and wide-awake he is, when he's in bed and I tell him them he starts yawning and his eyelids droop.)
Then you leave the room. Switch the light off, shut the door. She howls. You go back in, you stroke her (lay her down again if necessary), you say something like "Shush, shush, lovey. Time to go to sleep." You don't switch thelight on, you don't pick her up. It helps if the landing can be dim as well, to keep her room dim too.
Here you have to make a choice. For how long do you stroke her? If she settles, you could stroke her until she is calm and leave the room. Or you could stroke her until she is asleep - but she could wake in any case when you stop stroking her. And it doesn't sound like she's going to do that, anway. If she won't settle when you stroke her, then you have to leave the room. Your continued presence rewards and reinforces whatever she is doing. You want to reward her for settling down, not for bouncing around.
Whatever you do, she is likely to cry again when you leave the room.
So she is going to cry. So you go back in again. Lie her down, say the same "Shush, shush" phrase, do the same stroking, go back out, shut the door. Even if she doesn't settle down. You go in and out of her room as many times as it takes.
It could take several hours fir the first night, but it should take fewer and fewer repetitions night after night.
Listen to the crying. Is it an aggrieved whmper? You don't need to go in to her. Is she getting distressed? Go to her.
I used to go in at 20-30 second intervals at first. There is no need to leave the baby crying, but at the same time she has to be given the chance to sort herself out.
Sorry for the long post and for the telling you how to do it style. I could try to rephrase it, but then it would be even longer, and afirementione 3yo is now bashing downthe door of my refuge (the ensuite)!
HTH. Remember, it can seem like an unchangeable nightmare, and the first nights can seem to go on forever (not seem, they do!), but consistency and determnation will pay off, she may he angry but will not suffer, and you will all be better off in the long run.