NO. A rash indicates that your body is having an allergic reaction, and that the source of the allergy needs to stop. That kind of rash has the potential to become severe enough to cause your throat to swell so you cannot breathe.
As for having no periods, I am opposed to the forms of birth control that cause women not to menstruate. We have periods for a very good reason - to shed the uterine lining, as it needs to be shed, on a regular basis. I firmly believe that the women who are using those methods of birth control will have serious issues with such things as endometriosis and fibroids at mid-life, and problems with a thickened uterine lining - and even a tendency toward uterine cancer. Nature does what it does for a reason.