Yes, he is. I did his series for the core vax (tetanus, flu/rhino, EEE/WEE, WNV) myself, and he had side effects but they were manageable. Fever (103.3 at one point), loss of appetite, swelling at the site that all lasted 3-5 days. At the time I assumed it was maybe just that particular brand of vaccine, and made a mental note to use a different one next time around. The first round I gave in the neck and ended up having to elevate his food and water the next day, he was unable to put his neck down for a day or two. The second round I switched to the pectoral muscle, and he struggled with lifting the leg on that side when walking but at least he was able to eat and drink comfortably.
Ironically, that product was also manufactured by Boehringer Ingelheim, and was one I hadn’t used before - the Prestige vaccines, made by Merck, are my usual go-to but they were out of stock everywhere I looked.