I had this filler 3 days ago and now I have had some dizziness. Is this normal?

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.

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.