Yes, I agree with Elaine. I would call the vet back. Personally, I would wait on neutering until his symptoms are completely gone. Copying & pasting this from a website:
Nasal and/or ocular discharge and sneezing:
Live intranasal vaccines including the kennel cough vaccines (parainfluenza virus, Bordetella +/- canine adenovirus) and intranasal cat flu vaccines (felineherpes virus - FHV - and feline calicivirus - FCV) can induce mild signs of the disease that they are designed to prevent, with a watery ocular and nasal discharge and sneezing (occasionally coughing) being the most common signs. These signs tend to develop 3-4 days following intranasal vaccination.
When to worry:
Generally, these symptoms are self limiting and disappear within days. If the nasal discharge thickens and develops colour, changing from a clear, waterydischarge to a thicker yellow or green discharge, a visit to the vet is warranted. Greenand yellow discharges can be indicative of bacterial infection and antibiotic medication may be needed.
Note that it is possible for cats and dogs showing mild vaccine-induced respiratory symptoms to pass these vaccine viruses on to other cats/dogs in the household, thereby inducing similar mild upper respiratory tract symptoms.
Note that, in populations of cats and dogs with genetic immunodeficiencies (e.g. some purebred animal breeds), the use of intranasal vaccines may need to be avoided becaue of a greater risk of severe upper respiratory signs being induced by nasal vaccinations.