Is it normal to have menstrual symptoms without the bleeding from a period?

Yes. Ruling out pregnancy first, the "menstrual symptoms" are due to the drop of hormones effect at the end of the cycle. If the endometrium(lining of the womb) is minimal in length, than very little or no menstrual bleeding occurs.This is common in low dose contraceptive pills as away to prevent accidental implantation and the bleeding may be only "spoting" or a brown 1-2 day discharge.