3 weeks on Prozac and still getting body sensations and palpitations?

Hi, ereihs!
These are all side effects when first starting an antidepressant/anxiolytic like Prozac. They're usually mild and short lived resolving in several weeks. It sounds like you've ruled out any underlying cause so it's logical to assume that it's due to the medication.
These figures may help:
"Common (1% to 10% of users): Chest pain, palpitations"
"Common (1% to10% of users): Anxiety, depression, emotional lability"
"Common (1% to 10% of users): Paresthesia/sensory disturbances"
And:
"Side effects have been reported to be generally mild and transient. They are most common during the first 2 weeks of treatment and decrease in intensity and frequency with continued treatment. They generally do not lead to treatment cessation."
Your psychiatrist will be able to give you more information.
Best regards,
Wildcat