You can and should appeal your injunction, if you are not happy with the outcome. However, you must do so within so many days of the entry of the final order of injunction. Injunctions are created by statute and interpreted by case law (or precedent). But the law is usually pretty clear. The petitioner has to lay out certain evidence in order to satisfy the statutory requirements. If they do not do so, the injunction must be overturned.
A common problem is that there are so many injunctions heard in so many different courtrooms in Florida every day. VERY few of them ever get appealed. Most of the best cases that would be overturned on appeal never get overturned because the losing party does not have the money to fight it with a private attorney. There are no public defenders or free, court-appointed lawyers for injunction cases.
In order to appeal an injunction, you will have to hire a private attorney to file a notice of appeal. To prepare the appellate brief, the attorney will need the full transcription of the hearing or trial. That transcription can be expensive, depending on how long the hearing or trial lasted. Once the transcript is prepared, the attorney will use what is contained in it to prepare the appeal.
You cannot add additional information to the appeal. In other words, if it did not come out during the hearing or trial, you cannot bring it up in the appeal. That is another thing that most people are not aware of when they go to trial on a civil injunction. That is another reason having an attorney go with you is so important.
Judges are human beings. And human beings make mistakes. Just because a judge issued a final injunction in your case does not mean they were right. Often times, judges get it wrong or the record is insufficient to uphold a final injunction.
Many times injunctions are overturned by the appellate courts for a variety of reasons. For example, if a person presents a really good stalking case to a judge with only one incident of stalking, that is not enough. Stalking requires more than one creepy act. And even if the petitioner presents the bare minimum of two creepy stalking acts, both must create substantial emotional distress in the person being stalked. If the petitioner does not get that into the record, your injunction should be overturned by the appellate court.