If you feel like you're about to start your period but you haven't yet is that normal?

Yes: It is very normal to have the feeling like you are starting a period, prior to starting. These symptoms often precede a period. Also, it may be that your period is a "couple" of days late. This cycle may be slighlty different in the timing, compared to previous, but still considered normal. However, if you have had sex and you miss you period by a week or more, you should do a preganncy test.