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Because he has recently been at the groomer's, I would be worried that he has a respiratory illness that he picked up there. If the mucus from the nose is clear and he seems to be eating well and in good spirits, you can wait and see what comes of it. If the mucus from the nose is green or yellow, you will want to see the vet to find out what's going on. A little blood mixed with mucus is fairly normal and not always cause for alarm.
My other concern is that the nose was abraded when they administered the vaccine. Bordatella (kennel cough) vaccines are most often given through the nose as a spray. They spray it through the nostril. So he could have some irritation from that, especially if he wiggled when they did it.
I would keep an eye on it and see the vet if you don't see any improvement soon.