I am sorry to hear that your girl has vomited several times today, is shaking, panting and restless and is refusing to eat.
If something were stuck in her throat she would be gagging/coughing constantly.
While she sounds extremely nauseous and uncomfortable, given her shaking and refusal to settle, I do not believe she has anything stuck.
She is likely dehydrated because she has been vomiting, but if she is vomiting everything she takes in you need to take away food from him for now until he stops vomiting, and allow only sips of water.
In most cases vomiting is triggered by eating something they should not, too much table food, too many treats or something they find outdoors.
More serious causes of vomiting include toxin ingestions, viral or bacterial infections, a dietary allergy or sensitivity, inflammatory bowel disease, internal organ failure (kidney or liver disease), pancreatitis, Addison's disease, or a full or partial gastrointestinal obstruction. Since she is an older pup then an abdominal mass is also a possible cause.
Because she is vomiting so much and is so uncomfortable ideally she would see a veterinarian. I understand that may be hard to arrange on a Saturday night.
If a veterinary visit isn't possible for whatever reason there are some things we can try at home, but if she's not improving quickly she should see a veterinarian for an examination, some diagnostic testing, intravenous fluids and injectable medication to settle her stomach.
To try and settle her stomach you can give either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one half of a 20mg tablet per 20 to 40 pounds of body weight every 24 hours
These are both acid reducers and either one may help settle her stomach and get her feeling better and hopefully get her appetite back. They can be given for several days if necessary.
I would pick up all food for now and water for a couple hours to allow her stomach to settle after the acid reducer is given.
In a couple hours when you give her water make sure it is in small amounts only. If she drinks too much too quickly that can lead to vomiting. You can also offer ice cubes to lick. To get some electrolytes in you can offer her a 50:50 mix of pedialyte and water.
If there is no vomiting for 12 hours offer a bland diet mix of 1/3 boiled, minced, white skinless chicken or boiled, lean hamburger and 2/3 boiled, white rice mixed with some low salt chicken or beef broth to make it easy to lap up and swallow. If she refuses that you can offer a little meat baby food. If she refuses both then she needs veterinary care.
But if things go well and she does eat and doesn't vomit feed her the bland diet for 2 to 3 days then slowly start to mix back in her regular food, a little more at each meal. It should take about 5 to 7 days to slowly convert her back to her regular diet.
If she continues to vomit even with the acid reducers, runs a fever (more than 103F rectally), or has a lower then normal temperature (less then 99F), has a tense painful belly or if she refuses to eat she should see a veterinarian for an examination, diagnostics, injectable anti-nausea drugs intravenous fluids and supportive care.
Please let me know if you have any further questions.