I'm so sorry Gracie had this happen to her.......It looks like she had her first vaccine a bit too young for her to have had a second round at 10 weeks. To administer a vaccine safely to a pup a vaccine should be administered with nothing else at the same time, no deworming, no heartworm or flea stuff. The body is trying to already process the vaccine and anything else interfering with this process just add more stress to the body.
Vaccines are typically administered 4 weeks apart from each other. It's not the number of vaccines administered it's when. They typically do three to ensure the vaccine produced antibodies w/o being interfered with by mom's maternal antibodies. If your concerned with the pup having a reaction to the next vaccine you could always have a titer done to see if antibodies sre present. If there are then she's protected.
A lot of people like DR. J. Dodds schedule for vaccines it's a minimal approach....You can print this out and keep it for reference...
Vaccination Schedule Recommendations For Dogs
These are wonderful site to read about vaccines and our pups....
Truth4Dogs Top Natural Holistic Dog Health Care Book: Multiple Award Winner
You'll find some great advise on these sites..