Can I file a motion to be removed from sex offenders list?

I think your chances of being removed from the list completely are essentially zero.  You can file the motion, but I don't think it's realistic, to hope you can go from the Tier 3 list to entirely out of the registry.  What makes more sense, although I can't tell you just how much more, would be to apply for a reclassification.

Your first step should be to talk to an attorney who has some experience with this, or a criminal defense attorney who represents sex offenders, at the very least.  Getting any kind of relief under these laws is extremely difficult even for veteran lawyers;  if a reputable attorney tells you that he won't take the case because he's pretty sure you can't win, I'd let that be the end of the road on this one, at least for now.