I should note these are not discontinuation symptoms and are not symptoms I experienced prior to starting Prozac. They started due to the Prozac. I know it may take longer to disappear than other SSRIs due to its longer half-life.
You already got the answer -- Prozac stays in the system longer than other ssris. That's both better and worse -- it's better because it makes it easier to stop than other ssris. It's worse because bad side effects upon starting can last longer when you stop. And don't eliminate the possibility of some withdrawal -- everyone has a different experience. When you have a lot of side effects, it means you metabolized the drug well, and that means it got to your brain quickly. Metabolizing a drug well is important because if you don't it won't work, but it also means the side effects can be worse and you might find stopping the drug even early in the process might be harder than expected. It's always best to taper off a drug to avoid this as much as possible, just as it's always better to taper on them as well to see how they affect you. If this is it for you, no going back, and you're not immediately going back on another med right away, you might try taking fish oil, which helps with the dizziness in some people. You can also try taking a milk thistle based liver cleanser to speed the drug out of your system -- when drugs stay in your body for a month, like Prozac, it's usually because it's storing in your liver, so flushing it out can speed the process. Keep in mind that this isn't a good thing if it is withdrawal, because it might just make the withdrawal more intense. Three weeks is usually too short a time for a drug to start working, so there shouldn't be withdrawal, but again, you obviously metabolized the drug very well. And drink a lot of water or tea, again to speed elimination. Exercise can also help do this, particularly cardio. Good luck.