The red tint you're seeing might be due to lint from the floss as you pulled it out. There are a couple of things you could do. First, try "dusting" with an air can, like you use for cleaning computer keyboards. Next, you could always try to suck the fibers out with a vacuum, if you have a small enough attachment. Finally, test your remaining floss by soaking it in hot water, then squeeze it with a white paper towel to see if it's colorfast. If you're seeing red on the paper towel or in the water, you could run the floss through several rinses until the red stops bleeding. Then you could remove all of the stitches from your linen and use OxyClean or Spray & Wash to see if that takes out any remaining color out of the linen and then start over. I've also seen examples where some folks use OxyClean on a finished piece to remove excess color that bleeds from the floss. If you're wondering how I know this....
Don't let this get you down - you can do it! Every expert stitcher is an expert frogger.
Gorgeous.
That red! Your stitches are immaculate.
Very pretty