I am sorry to hear you are worried about Sadie. My name is Rebecca. I am a veterinarian and will do my best to help.
If she has diarrhea and vomiting from spoiled food, she may be better once it is all out of her system. If she continues to vomit, you can try giving Pepcid AC (famotidine) at 1/4th of a 10 mg pill, twice daily. Probiotics (beneficial bacterial supplements) may also help, especially ones made just for cats like Fortiflora or Proviable.
Try to keep her hydrated by offering broth, Pedialyte as well as water.
If she is still vomiting tomorrow, then seeing a veterinarian is best. We always start with a good physical examinination, which at my clinic is around $60. It may be more or less in your area. Then we might recommend medication, Xrays, or blood tests depending on what we find.
Check her gums; are they pink in color? If her gums are pink, that is a good sign. If the gums seem pale, then I am worried this could be more serious.
You can check her for dehydration: Gently pinch skin over her shoulders and let go. It should go right back into position in less than a minute; it it takes longer she is dehydrated and probably needs to see a veterinarian to get supplemental fluids (IV or injected under her skin).
Let me know how she is doing and what else I can answer. Rebecca