Immediate dizziness after receiving a filler is probably from "nerves" and patients can feel lightheaded. If you are not feeling great a few days after this minor procedure, you may want to see your internist for a check-up.
Dizziness 3 days later after a filler is unlikely due to the filler.
You should see your GP doc for checkup if the dizziness continues but it is unlikely due to a filler 3 days ago. Dizziness when getting injected is due to the vasovagal phenomena from seeing the needle or the injection rather than the material being injected.