i'm 5'11 so i would still be a tiny bit taller than you but in my opinion i like girls to be a few inches shorter than me, it would be a turn-off for me personally but i'm sure other people would like it.
No, your never too tall to wear heels. Guys don't mind if girls are taller. Guys are into tall girls mostly because if their long legs so your fine. Feel good and proud to wear those heels and look good.