I may not be the best person to be giving advice, but cutting yourself on your neck/throat area has to be extremely dangerous. For starters cutting is never a way to solve or even avoid your problems. Next to cut yourself where you are thinking about you would have to be looking into a mirror, or just cut blindly, either way the risk of accidentally slipping a tiny fraction, you say you don't want to kill yourself but you are proposing something that is at least as dangerous as Russian Roulette, using a razor instead of a gun.

Just an idea, if you do cut yourself there, you will most certainly end up in the emergency room, and from there to a mental hospital. Why not skip the cutting and the emergency room and get help NOW.

I hope that you can find the strength to reach out for help