The main difference between Cymbalta and Prozac lies in the neurotransmitters they affect in the brain. Prozac affects Serotonin almost exclusively, while Cymbalta, one of the newer formulations, affects Norepinepherine in addition to Serotonin. I am guessing your physician switched you because Cymbalta has been known to create energy, and may have amped your anxiety slightly. Prozac may be a better alternative for tending to the anxious symptoms.
As for your concerns regarding side-effects, Prozac's will be pretty similar to Cymbalta's. You will probably have an upset stomach for the first week or two, and may have trouble falling to sleep. Too, Prozac has been known to interfere with orgasm and sex drive. But the most serious side-effects don't typically have anyhting to do with seizures of heart attack - in fact, Prozac is one of the most mild SSRIs in the event that you skip a dose or two ("discontinuation syndrome"). The only really obnoxious side-effect that your doctor should know about right away is if you develop a bad rash after taking the medicine. Otherwise, Prozac is relatively safe.
Heck, it has been around since the mid-1970s, so it has the most proven track record of any anti-depressant. Seriously though, I understand that with anxiety, you tend to focus on the potential negatives. I hope I put some of your fears to rest. The Prozac may or may not help the anxiety (everyone has a different chemistry set between their ears), but it should be safe for you. And as always, make sure to talk this over with the prescribing physician as well.