How do you prevent image compression when saving pictures to iPhones?

So, I'm a digital artist and I find that the filters found on iPhones are very nice for color correction or just to make the thing look prettier, because my monitor has a problem of displaying everything too blue (so the actual image turns out to be super saturated and pink/yellow). However, so much of the image quality is lost when I save the pictures to my iPhone (I usually email the pictures to myself). This is a problem, because I love the effect the filters give me, but I can't use those final images for prints because the resolution is so small. Is there a solution around this?

Calibrate your monitor. Read the manual or go online to find the directions on how to do this. A color checker may be required. A phone will always compress your photos - the computer won't unless you save the file with compression. Read up on how to deal with that monitor.