Hello I am Dr. Joey. Thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 16 years of experience. I look forward to working with you.
I'm sorry Josephine is experiencing this. First, for the coughing/gagging, there is no an easy way at home to remove something from the throat. Certainly possible she got a blade of grass trapped. The best you can do is try to look (but the tongue is usually in the way; for us to look requires sedation) and you can encourage her to drink which may clear any actual foreign object causing irritation. Now, this cough/gag may not be from anything stuck in her throat, though. It may be she has true throat sensitivity such as could come from tonsillitis or a polyp/tumor or other infection. So, if this worsens or does not resolve within the next day you should have your veterinarian perform an exam.
The grass eating, if new, usually indicates a level of nausea. At home the only easy and safe thing you can try is famotidine (pepcid AC) which you can purchase at any people pharmacy (you would give 20mg every 12 hours). No anticipated side effects and does a great job soothing a sour stomach.
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