Poor baby Rowan! I hope whatever it is clears up quickly, I hate this sort of thing when they're so young.
Lark had a similar episode when she was about that age, not so much vomiting, it moved quickly to diarrhea. When I called the vet to say I wanted to bring her in the phone consult person started asking me how long I'd withheld food, have I tried this or that. No, she's 14 weeks old and I want to bring her in as soon as possible, today. I'm with you on getting things under control ASAP.