Prozac anxiety is a side effect of the drug. It can be especially disconcerting, if you are trying to wean yourself off of the drug. Even as the levels of Prozac go down in your system, you are still likely to think about suicide, and you may even try to act upon it. So, make sure that you are closely monitored by your physician. If your child is on Prozac, anxiety levels should be monitored, because suicidal thoughts can be even more intense for teens and younger children. Also, if you or a family member is taking Prozac and other medications at the same time, you should be more closely watched for possible life threatening side effects.