Will my fluoxetine induced insomnia go away with continous usage or worsen, or should I stop taking?

Hi, eddon!
How long have you been taking the medication? Side effects generally resolve within just days to several weeks for most people. Again, depending on how long you've been taking it you definitely shouldn't stop it abruptly or change your dosage.
You should always report side effects to your health care professional so give your doctor a call and get her/his professional advice.
Best regards and I hope you're getting your sleep again very soon.
Wildcat
"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."