Help me save my bedroom furniture

Nothing. If the moisture wrinkled the paper and swelled the flakeboard, you're out of luck. Go find a table cloth whose design you like. Have a tailor cut it to size and hem it. Spray with Scotch Guard to repel water, if you can't stop yourself from getting it wet.

I was going to suggest kitchen cabinet "trim 'n stick" would probably look as good as the original did...but decided I'd refrain. :)

I did use the "trim and stick" stuff on some shelves in a computer desk that had gotten messed up with digs from screws from some equipment. Sanded things smooth, and put the stuff on. Only trick was getting the bubbles out... used a credit card. Razor knife for the edges after it was in place. Probably better than what was on there in the first place...

I was being only half-facetious... :)

The other alternative if the substrate isn't _too_ bad is laminate (as in Formica-type, but wouldn't seem the pieces would be worth the expense/trouble...

Find a peel-n-stick which matches closely enough, sand the existing tops smooth, apply some shellac to seal the flakeboard, sand again, thoroughly clean the surface with a tack cloth, apply the peel-n-stick, roll or press to ensure a good bond, trim carefully. Done properly it won't look any worse than the original and will probably be more durable because of the shellac will substantially protect the flakeboard.