It happens to some people, whether they have MVP or not. The shot contains epinephrine, which is adrenaline. It helps the Novocain work better, but it can cause all of the symptoms you described.
Next time ask for an epinephrine-free anesthetic. All dentists keep them on hand for patients who are sensitive to epi.
Make sure and tell the dentist next time to give you a shot WITHOUT epinephrine. I get these shots all the time when going to the dentist, my heart never races or skips, but in the past when I had the regular novacaine shots, my heart would race, skip, I'd be nauseated etc.
I have heard some patients have a heart reaction to novacaine. I have also heard that there is a novacaine without phenylephrine which does not cause the same effect but I'm not sure by any means.
I would suggest checking with the dentist and good luck.