You wrote that you're already putting vitamins in her water. I'm wondering if it's too much of a good thing. These are just some ideas, I don't feel like I know how much she's been getting. But toxicity or infection keep coming to mind as possibilities. I wish I could think of a way to narrow down the culprit. This can be so frustrating and scary.
The charcoal, I am told, binds to toxins and helps as they pass out of the body.
I think just regular clean water will help most.
Vomiting may indicate there's blockage in her digestive system.
Some people recommend epsom salts in water as a laxative. Be very, very careful if you decide to try that. If she did (some ducks surprise me with the odd ways they have to get into trouble) ingest a sawdust pellet, I suppose it could have swollen up in her little tummy and be causing some blockage. So charcoal water might possibly help with that.