Dogs sometimes, but rarely suffer reactions to shots. I highly doubt that those problems that started a week later are related. Have you asked the vet about it? Most vets are too ethical to try to cover up a bad reaction. You might try doing a search at
American Veterinary Medical Association Who knows what misinformation may turn up on a site somebody Googled up and then didn't give her source.
I don't know where your are, or what the practices are in Canada, but in the USA, it is common to give the last round of puppy shots at 4 months, and then an annual booster shot that covers a number of things. Usually the vets don't give a separate distemper shot.