Prozac takes a while to build up in your system. In addition, it will help manage your systems - you still need to work on the other issues you have, such as your anger toward your family.
Determine what upsets you about your family and ascertain if there is anything that you can do to help the situation.
An example would be - your dad always gets on your case when you get home from school to get your homework done right away. You would rather relax and then deal with it.
One solution would be to talk to him about a compromise. If you could have 30 minutes of down time after school, would he go for that?
That's merely an example. In addition, find someone to talk to about issues that you're having and if they can help you work through some things. Good luck.