Need help with relaxer?

When I first started getting a relaxer, I got Revlon Regular with lye because I was told that people with no-lye relaxers had issues with losing their hair. I would like to switch to no-lye, but I'm being told once again that I could lose my hair. Is that true? Are there any issues I should be aware of? Also, my hair is really thick, and with the regular, it still doesn't look like I have a relaxer. I have sensitive skin, that's why I only use a regular. I have to use a flat-iron to get it straight. If anyone has any suggestions, that would be fab. Thanks!