Is it normal if my period came twice a month? Why does this happen?

No. The normal menstrual cycle varies in length from 21 to about 35 days. If your periods are starting closer together than 21 days from the start of one to the start of the next, then you are not ovulating regularly - or you have some other problem, such as infection, polyps, adenomyosis, fibroids, etc. Either way you should see your gynecologist for evaluation and treatment.