A vaccine is designed to produce an immune response of the right magnitude. Too low and it doesn't work, too high and it'll cause damage. At least one of the vaccine candidates in development was put back to the drawing board because the immune response wasn't strong enough. So this is not an area that is entirely predictable, you have to carefully test this to know if it works.
I'd also be very careful about the inhalation route. Inhalable insulin is a well-known failure, in part because of side effects due to the inhalation. And that is a protein that isn't designed to activate your immune system.
I also hope the synthesized peptides were carefully purified, you really don't want to inhale e.g. residual trifluoracetic acid.