I'm myopic (20/80 and 20/100). Could the shape of the eye caus you to see more halos or starburts?

Possibly. With correction, many of those images should be reduced or disappear altogether. There is a phenomena called spherical aberration which has to do with the topograpjhy of your eye which may leed to above described images. Also if your eyes dilate at night you may see halos around lights. Uncorr4ected astigmatism may be another cause.