I am sorry to hear you are worried about Owain. My name is Rebecca. I am a veterinarian and will do my best to help.
These could be enlarged lymph nodes, and might get smaller on their own after a little while. Since there is one on each side, that is the most likely thing. Since he is a kitten, cancer is unlikely, but feline leukemia infection is a possibility. Has he been tested for feline leukemia?
I agree that doing FNA, fine needle aspiration, is the next step: insert a small hollow needle into the lumps to get some cells to examine microscopically. That should tell what these lumps are, and if they are anything to worry about. I would also ask your veterinarian about a feline leukemia test if they turn out to be lymph nodes.
It is possible that in the immune system's response to the vaccination, the lymph nodes temporarily enlarge.
Let me know what other questions I can answer, and if this was helpful!
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You are welcome, and thank your for the bonus and great rating!