My daughter was always clingy and got extra clingy towards the end of my second pregnancy, I was so worried about how she'd be. Wasn't to the same level - no vomiting but hysterical crying. I found if she didn't see me go she didn't get upset so where possible I got Nanny or whoever to come when she was asleep and luckily my waters went in the middle of night! I chose not to bring her to the hospital to see me and the baby to avoid the upset of having to leave, although it upset me to not see her - it was the lesser evil! She has been a dream with him. She didn't react badly at all and even runs to get his soother if he cries etc. All we done was get her a little teddy as a gift and I make a point of if he gets agitated or upset saying to him that I'll be with him in a minute I'm just helping her, so she isn't always second and hears the same for him as we tell her, tbh sometimes he's fine and I just say it if I think she hasn't heard it in a day or so. I also keep saying he's smiling at her etc
No idea if any of it actually helped, I did read online that it's a hormonal thing that they pick up on towards the end of pregnancy. I know a few people who also had super clingy babies/toddlers and like ours, it's like they just snapped out of it when new baby arrived. One was actually in labour and the baby wouldn't go to bed unless mammy rocked him to sleep! As soon as she got him down straight to hospital and baby was born within an hour! I've no real advice unless you try what we did but try not to worry and hopefully it'll be ok.
In the same position although mines not being so extreme but would appreciate some advice too