Hi,
Since you're going to the hairdresser, tell her that it has only been 2 weeks and see what she says. If it were me, I couldn't dare relax my hair again so soon, I know it would all fall out. But my hair is thin. Since yours is thicker and you say the first relaxer didn't take, then maybe the strands of your hair didn't go through the relaxing process enough and will not be harmed by re-relaxing again so soon. Again, tell the hairdresser the whole story and see what she says. Good luck!!
Have a blessed day!!