so I'd been designing illustrations on my HP laptop - all the images looked exactly the same colour-wise on both my laptop and my Samsung phone. Now recently I got a Lenovo Ideapad and noticed the colours look all different - eg. #eeeee6 looks cream-ish on my old laptop and phone but on the Idepad it looks quite grey. I'm a designer so the colours are quite important to me - is there a way to resolve this? I've tried switching up the display settings but nothing seems to work. Thanks!
Basically, you can't fix this. You can certainly do some things to make differences less noticeable (see link in @Nash's comment), but you can't fix the basic issue - that different display hardware will give you different display colors.
And even beyond just the hardware differences, users will adjust their displays different ways, such as more or less contrast. And many monitors have "color control" or some variant like that.
And then there is the whole aspect of the user's perception of colors. You may think the two look different because you are a designer, but others may not notice the difference, or even care.