Believe me, there's nothing wrong with the Fatip Piccolo. In fact it's probably a better idea than the DE89 because it may cut closer therefore less potential passes and irritation. My son has sensitive skin and preferred the Piccolo to the Rockwell 6c on 5 or 6. I find it quite mild, though I use a R41 which is more efficient.
What I'd suggest is:
- Shave every 2 days until the burning stops.
- Face lather with plenty of product, and keep adding water until the lather is quite sloppy.
- Use as little pressure as possible and be satisfied with a reasonably close shave on the irritated areas. They should get better with time.
- Use a Gillette Silver Blue until this clears. That's the smoothest blade I know while still being very sharp.