Floating and something like a black fly in my right eye 3 weeks after LASIK

I do not think this is likely connected to your LASIK, but if you have a sudden onset of more floaters, and see a "fly" in your vision, it sounds like you have had a vitreous separation.  This is usually benign, but if recent onset, and especially if also associated with a sudden increase in floaters, you should have a dilated exam to be sure that there is not an issue with your retina that if left untreated could lead to a retinal detachment.  This is unlikely as I said, but merits an evaluation.