My heartfelt condolences on the recent loss of your 3 year old male kitty to kidney failure. I'm sorry your 4 year old girl and the others, are grieving, but this is to be expected. Grieving and the big change in your feline household population can be taking a toll on your girl who threw up bile. This could be due to stress, diet, or an underlying medical condition.
She could have eaten one of the other cats' food, which didn't agree with her, she could have allergies to some of the contents in her current food, she might have ingested something she shouldn't have, or she could be producing excess stomach acid or have acid reflux, which leads to nausea. For the moment, you can give her 1/4 of a 10mg. tablet of the OTC acid controller, Pepcid AC (generic =Famotidine) every 12 hours and see if this will soothe her stomach and quell the nausea. Here is more information:
Put her on a bland diet of plain, jarred, infant baby food chicken, containing NO onion or garlic products---Beechnut Stage 1 Chicken is a good one. Serve her small portions at a time, as long as she's not actively vomiting. You can finger feed her, instead of putting it in a bowl or on a plate. Also, encourage her to drink.
For the stress that she is encountering, with the addition of other kitties, you can get some Feliway plug in diffusers; these emit cat calming pheromones and have no scent to humans:
If she only vomited once, that's good, but if she continues to vomit on a steady basis, she will need to be seen by a vet, to determine the cause, based on a physical exam and lab work. The vet will also give her an injection of an anti-emetic, to help with the nausea and vomiting.
I hope all will be well with your furry girl! Please let me know how she's doing. Thanks!
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