Straightening damages your hair and damaged hair breaks, so even if it's growing it won't look like it is because all of your ends are snapping off. Take this from a girl who was straightening her hair and trying to grow it for around ten years lol. I never got past shoulder/arm pit length.
Now that I'm natural my hair grows at the speed of light ... well, okay, slight exaggeration, but it grows A LOT quicker. I recently cut off all my straight ends and my hair was earlobe length and now it's shoulder length and it's only a month later. Point being, healthy hair grows and damaged hair just snaps, so you need to start nurturing your hair.
Use oils like coconut oil that really penetrate your hair and moisturise.
Cut out the sulfates.
Deep condition once per week.
Cut out heat or use it A LOT less.
You should try just doing two pigtail plaits in your hair overnight for nice, loose and defined waves. Or other heatless styles for curls. That's what I did while transitioning. It'll stretch your curls to waves, which is what you said you were aiming for and help you to cut the heat