For intarsia knitting, which is what your's seems to be--the heart in the middle of a solid field, you should have two strands of white. One up to the heart, then the pink for the heart, and then another for the other side of the heart.
You shouldn't have to knit with both hands--I certainly don't. You'll knit across with the white up to the pink, knit with the pink, and then again with the white that's on the other side of the heart. Just make sure you hold your yarn over so you can bring the new color up from under it to avoid the hole.
When you get to the top of the heart where the point is in the middle, you might want to attach a third strand so you won't have to carry any white across the back of the heart 'bumps.' When you're done with the heart, you'll be back to all white and just have ends to weave in from the other strands.