I have to agree with the other posters that a delayed reaction from vaccines is rare, but it certainly can happen, especially if it was a type IV delayed hypersensitivity reaction. It sounds like you were certainly within the 48 hour window for that to happen.
I hope she is doing better now.
Ghilly has some good ideas about titer testing, just be sure to speak with your veterinarian about that before proceeding. There are some concerns over what the levels "truly mean" with respect to whether or not the pup is protected. Another consideration is to "space out" the vaccines so that she is only receiving 1 at a time over a period of several weeks when her vaccines are due again. That can help to minimize any potential reaction.
In any case, make sure your veterinarian noted this in the medical record so that they are aware next time she is in for vaccines.
I am sure our doctors over in the Ask a Vet expert forum might have some ideas for you as well. You might pop over there and post this same question to them.
Good luck...keep us posted!
Vomiting and diarrhea can be symptoms of an anaphylactic reaction to a vaccine, however it's extremely odd for anaphylaxis to occur two or three days after the vaccine is administered. Normally it's almost immediately afterward, and almost always within the first 24 hours after being given the shot. In addition to the vomiting and diarrhea she would have had very pale gums, her pulse would have been very weak and her heart rate would have been very rapid. Normally the antidote for anaphylaxis is an injection of epinephrine, which should be administered preferrably within a few minutes of her having the reaction.
What type of vaccination(s) did she receive? Anaphylactic shock can occur after any type of vaccine but is far more common when it's a killed vaccine like a rabies vaccine or a vaccine for leptospirosis or canine coronavirus. The reason for this is because killed vaccines have more bacteria or virus particles per dose and they have adjuvants added to assist the immune response. These adjuvants can also be responsible for the anaphylactic reactions.
Just to be on the safe side, when she comes due for her vaccinations again you might want to have the vet draw blood and run titers first to see how much immunity she still has before just going ahead and vaccinating her again. If she had her full set of puppy shots and her one year booster, and now she has had this year's shots, as long as she is healthy and her immune system is not compromised by anything, chances are good that her immune system will be equipped to protect her for a good couple of years before needing to be vaccinated again. If this is the case, I would avoid vaccinating her for as long as possible, and each time she came due for vaccinations, just run titers and make sure she still has sufficient immune response. As long as that's the case, she won't need the vaccines and you won't need to worry about a possible reaction.
Ghilly
I think its highly unlikely after 3 days your dog would have a reaction to the shots she received. Usually reactions to shots come a few hours after. I think it would be more likely that your dog either picked up a virus from the vet, she ate something or was she at a park or dog run recently? She could of picked something up from the park or dog run. If you think about it there are sick dogs in and out of your vet all the time. You bring your dog in and they can easily pick something up. May sound crazy but I always wipe my dogs paws down when we get back from our vet or dog park just to be safe.
Try not to worry too much, you can make yourself crazy trying to think about the causes of how your dog got sick. You are taking care of it now and thats what counts.
If she is not better, I would bring her back to your vet.
Is she an indoor, or outdoor dog? Could she have eaten anything in the house? Around any strange dogs?
Was she current on her shots prior to this?