I think the saying is pretty accurate - I feel pretty much as you do when one of my dc is having a bad time. BUT I think your dd neeeds to learn some coping mechanisms. It's really not fair of her to be offloading all her feelings to you quite so often, ignoring your MH. She must realise that her emotions burden you?
Lots of negative things will happen to her - break-ups, fall-outs, losing jobs, not getting jobs, bereavements, accidents, arguments - and she has to learn how to cope with them in a way that doesn't involve her obsessing over them or leaning too heavily on you for support.
Your dd does sound quite self-asborbed and negative - one of the side-effects of depression/anxiety, I know - and this is something I'd bring up with her when she's feeling stronger.
Get her to be more positive - remind her how tiring it is to live with someeone who's always 'glass half full'.
The thing is, your worrying about her won't make a blind bit of difference; the end result will be just the same as if you hadn't spent a single second worrying about her, so try not to. I realise this is easier said than done!
Ensure that she's taking the meds she needs - they will kick in, and they should help - and counselling might help you both.
I'd also suggest getting her to help herself: not too much social media, see real people, eat healthily, not too much alcohol, get out in the fresh air, mindfulness exercises to help her focus on the positives - these will all help her more than being in her room will.
Does she have friends she can talk to? Does her uni have studcent pastol care? Can they help? Do you have RL support?