Unfortunately, this could be either a medical issue, or caused by stress, or possibly even both. Cats that are under stress are more likely to develop medical problems. Urinary tract infections, early kidney disease, diabetes, and more can cause the signs you have seen. If she continues to vomit I would definitely recommend a visit to your veterinarian to determine if there is an underlying medical issue.
Its possible she vomited because she ate too quickly, so if she doesn't do so anymore then you can try a few things first to see if they help her litter box problems. Changing the location of the litter box could be what triggered her to start this behavior. Because you can't put it back where it was originally, I would add one more box. Cats that have been fine for years will suddenly decide they want to urinate in one box and defecate in a different one. Even if you have to put them side by side I would still do this.
One product that may help her is Feliway. It consists of calming pheromones, and was specifically designed to help cats with inappropriate elimination problems. It comes in a plug in diffuser or a spray that you put right on the arenas she has defecated on. Most larger pet stores carry Feliway. Here is a link to their website:
Here is a link to a page that may have some additional ideas for you to try:
If these ideas do not help, or if she should develop any other symptoms such as loss of appetite, lethargy, etc. then I would recommend a visit to your vet right away.
If you have further questions let me know. If this answers your question please click accept. Thank you and best wishes.