Why is my dog sick and lethargic after taking an antibiotic pill?

Hello and thank you for your post! Speaking from personal experience, this used to happen to my dog as well. I would give him his capsule and sometimes it would get stuck under his lip and it would partially dissolve releasing the powder in his mouth. He would shake his head and foam at the mouth because of how bitter the powder was. He never got sick because of this and the powder generally will not cause any irritation it is just very bitter and distasteful. I would think that the antibiotic itself would be causing him to feel sick if he managed to swallow some of the antibiotic on an empty stomach. It is also possible that it has nothing to do with the medication that was administered and is completely something else that has led to him feeling sick. Since you have an appointment with your veterinarian, I would wait and see what the physical examination shows and possibly have Joel's blood tested. I hope this helps! Please let me know if you have any other questions and I would be more than happy to answer them for you.