Good Morning and welcome to Just answer. I am Dr. Loretta, a licensed veterinarian and I am happy to answer your question.
It is not unusual for baby goats to be so stressed that they come down with an upper respiratory infection and diarrhea due to the digestive disturbance secondary to this stress of changing environment and change of feed.
The best thing to do as long as Thomas is still eating well, is to give him an electrolyte solution that can be purchased at the farm supply every 4 hrs to be sure that he remains hydrated. You can give him Penicillin G that also can be purchased at the farm supply , 1 cc per 20 pounds daily for 5 days.
Apply Artificial Tears to his eyes every 4-6 hrs that can be purchased over the counter at the pharmacy to remove any irritants and bacteria that may be causing this discharge.
If he goes off his feed, then have your vet examine him since he may require more intense treatments.
Does that make sense to you?
Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please Reply so I can clarify for you
Sincerely, Dr. Loretta