Like ALL drugs Prozac (fluoxetine) does have side effects however in the vast majority of people side effects are mild and tend to go away over a few weeks.
The most common side effects include:
nausea, headache, insomnia, nervousness, anxiety, diarrhea, dizziness, dry mouth, tremor, sweating, constipation, and flu-like syndrome.
Should she experience them they normally go away within 2-4 weeks.
Serious and EXTREMELY RARE reactions include:
Serotonin syndrome (an extremely rare problem almost always due to taking multiple serotonergic drugs), withdrawal syndrome (this occurs in under 50% of LONG TERM users. If the drug is stopped slowly there should not be a problem), mania (may be an indicator of bipolar disorder rather than depression), seizures, hyponatremia (abnormally low level of sodium in the blood; associated with dehydration), hypoglycemia (low blood sugar), serum sickness (allergic type reaction)
anaphylactoid reactions (severe, potentially life threatening allergic reaction), and severe rash.
It is also very important to note that the principal serious side effect to closely monitor for is an increase or development of suicidal ideation and thoughts. People 24 and under have an increased risk in having suicidal thoughts HOWEVER there is no indication that using an antidepressant increases rates of suicide (only thoughts of suicide). Actually suicide rates are lower when people with depression use antidepressants at any age.
I know a lot of the side effects sound scary and your immediate reaction may be to take your daughter off the medication. But please don't let the side effects scare you, your daughters doctor (the expert) feels that taking fluoxetine is appropriate and that the risks are far outweighed by the benefits. And all drugs have very scary and serious side effects, even looking at the official information about paracetamol side effects could scare you.
Also if you don't understand the situation you need to talk with your daughters doctor until you do understand. You should also talk with your doctor and ask her what she thinks and about her depression. You should never feel left in the dark when it comes to your children's health.
As some people who have answered have mentioned therapy is an option and using both medication and therapy has been proven to be the best treatment. However it is NOT rare or unusual for teens to be prescribed antidepressants (in fact The UK government recommends fluoxetine for teens with depression and/or anxiety) . Awareness and destigmatization are the reasons that depression is being evaluated for and treated, if required, in teens. Although therapy alone may be appropriate often it is not. Therapy often takes a significant time to begin to work and many people need to have faster relief.
Below are several links from multiple well respected governments, medical institutions, and companies in The US, The UK, Canada, Australia, New Zealand, and South Africa about Fluoxetine.
http://www.nlm.nih.gov/medlineplus/druginfo/meds/a689006.html
http://www.netdoctor.co.uk/medicines/100002193.html
http://www.nps.org.au/search_by_medicine_name/cmi/genrx_fluoxetine
http://www.merck.com/mmhe/sec23/ch286/ch286c.html?qt=fluoxetine&alt=sh
http://pi.lilly.com/us/prozac.pdf
http://www.lilly.ca/servlets/sfs;jsessionid=00826E2266A0C19525590C5C6737BE72?t=/contentManager/selectCatalog&e=UTF-8&i=1233164768976&l=0&s=iBxTi05ufMKzEEKLZG&ParentID=1246635267998&intro=1&CustomerID=0&startRow=0&active=no
http://www.medicines.org.uk/EMC/medicine/22424/SPC/Fluoxetine+20mg+Capsules/
http://home.intekom.com/pharm/apotex/ap-fluox.html
http://www.medsafe.govt.nz/consumers/cmi/p/prozac.htm