Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I am very sorry to hear about your pup Luna's eating grass and gulping/coughing.
It is possible that she has a foxtail awn stuck, but because her behavior started with eating grass I think that may not be the full issue. There was a reason that she started eating grass in the first place. I suspect that she has gastroesophageal reflux.
Dogs with nausea or gastroesophageal acid reflux often eat grass or foreign material to make themselves vomit. They will often swallow repeatedly, gulp and gag trying to soothe their nausea and acid burn. If they can rid themselves of whatever is irritating their stomach that way then all is good.
But when they are repeatedly eating grass and gulping and continue to be uncomfortable then we need to stop them from eating any more grass. It becomes a vicious cycle where the more they vomit the more their stomach acid burns their esophagus and the worse they feel.
Possible causes of reflux and nausea causing grass eating include a change in diet, dietary sensitivities or allergies, or eating things that they should not like too many fatty table scraps or garbage, bones etc. Addison's which is a poorly functioning adrenal gland is another possibility for waxing and waning vomiting and nausea. Since she's an older pup metabolic organ failures (kidney or liver disease), pancreatitis, inflammatory bowel disease or even infiltrative cancers are possible causes too.
Has she eaten anything she should not have recently (toy pieces, bones, garbage)?
Any changes in food or treats?
You can give her acid reducers to try and settle her stomach. Either:
1) Pepcid-ac (famotidine) at one half of a 10mg tablet per 10 to 20 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at one half of a 20mg tablet per 20 to 40 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle her stomach. These can be used long term if necessary as they are very safe.
I'd also pick up her food and water for now. A couple hours after giving one of the acid reducers you can offer small amounts of water or ice cubes to lick.
No food for 12 hours. Small amounts of water only.
After her food fast then start a bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 boiled white rice. Give small meals several times a day. Feed the bland diet for several days, then start mixing in her regular diet and slowly convert her back.
If her vomiting or nausea continues then she may need injectable medication from her veterinarian to get her stomach upset under control and she should have some bloodwork checked for underlying organ disease.
So watch her for continued gagging/reflux even with the acid reducers, blood in her stool or vomit or a fever (more than 103.5F rectally), a tense painful belly or lack of appetite after her food fast. If any of those occur it is time to seek hands on veterinary care.
Please let me know if you have any further questions.