nekretoucher,
welcome to
RP.
i'm afraid the current digital system makes this problem more of a problem than it shld be. because digital creates various colors from other colors you get the problem that the red rose seems like the only red in the image, when in fact, it isnt. there's actually lots of red in your image. we look at it and we go, that shld be easy to change. but, when you apply a filter or tool to affect the reds it affects all the reds in the image, including those colors that are partially created from red.
so, that means you have to isolate YOUR red out from the other reds in the overall image. and that means selections or masks. i used the magic wand set to color mode and simply made a selection of the red in the roses. if you get that right, then it's easy from there on.
you simply desaturate, using whatever you have that will do that, hue/sat adjustment layer, fast fix, or whatever and also lighten at the same time. this will allow you to pick whatever white you want, whether ivory, eggshell, pale, etc. i simply used my own 32 band gray plugin to desaturate and lighten.
once you've got that, you can then do any final tweaks you might want, like anti-aliasing the selection, contrast adjustments, or other global adjustments if desired.
also, your image is quite small and only at 72 dpi. you'd avoid some other problems by working with larger images at higher resolutions.
it's a nice picture and well worth some tweaks, so, good luck
craig