Welcome to Justanswer! I am Dr. Altman and happy to assist you both today!
First, congratulations on your new addition! I hope you have many happy years together :)
Typically kennel cough will appear within 7-14 days of adoption but it cannot be ruled out. Often kennel cough is described as a cat with a hairball cough so that is also something that doesn't go with this diagnosis.
I agree that it is possible there is something in his nostril and/ or he was bit or inhaled a bug that is causing him distress.
There are some home remedies that can help reduce the sneeze and give relief
1.) The steam of the shower when the cough is severe or constant
2.) A little honey three times daily can help soothe
3.) If you have a humidifier or nebulizer that would also be wonderful to use in this situation
4.) Ensure you are giving an appropriate benadryl dose of 1 mg/ pound. I am happy to calculate this for you based on Zoro's weight. This will help reduce the itchiness in his nostrils and hopefully allow him to rest more comfortably
I hope this information makes sense! If the sneeze progresses to nasal discharge with color, there is lethargy or a reduced appetite then it would be best to have a veterinary exam to ensure antibiotics are not warranted or exploring for a foreign body is not necessary
Please let me know if I can be of any further assistance to you both!
If you have more questions or if I can help in any other way, please do not hesitate to ask! If you would like to accept my answer, please press RATE OUR CONVERSATION (I am not compensated in any other way). Bonuses are always welcome. Thanks!