It can sometimes happen that they get a little lump where the vaccination was given. As long as it isn't weeping or scabby, then the little feller should be okay, but I would mention it to the vet if the swelling hasn't gone down by the time of his next visit, as they may decide to vaccinate in a slightly different spot to avoid discomfort.
Very occasionally, cats can develop an adverse reaction to vacs so bringing it to the attention of the vet if it hasn't gone away by the next visit will just ensure it's properly checked.
What's the new family member called? (I cant see the details in your avatar on this computer for some reason!)