Animals that have a tendency to lick or chew their feet generally have airborn allergies.
Your puppy most likely spends her licking time on her front feet. Pay attention to see if she sneezes around smoke of any kind or perfume/cologne. If she's really sensitive you'll notice sneezing with just about any strong odor or any odor she's not familiar with.
Reactions to vaccinations are generally only a mild swelling at the injection site. Depends on the vaccination of course. Anything other than that, though, and she should be checked out immediately. At 12 weeks, though, she would be done with her vaccinations for the year and likely any reactions would have subsided by now.
If she doesn't appear to have any type of airborn allergy you're probably looking at a behavioral problem. Then again at that age she may simply be teething and finding chewing her feet to be quite an amusing game - especially if she gets a reaction out of you by doing it.
Pay attention to her sneezing and sniffing, though - and check the allergy index on the days she seems to be especially "active".
Our husky has allergies and during the spring/summer months she is merciless on her feet - mainly her front but she will go after the rear, too. She hasn't done any damage - she's never broken the skin or pulled fur or anything of the sort. Never even left herself sore (at least not that we could see). And she gets a kick out of us telling her not to do it. =)