I was looking at the section for the older Supra's here in this forum. Some of the owners put pictures in so you can tell if yours looks like their older Celica Supra or the later model. I sounds like you have the 86.5 on up though with the 3ltr 24 valve engine, but as far as I know they never came with the extra bolt on fender flares....so it makes it sound like the older version.
Pictures would help...........
Russ