Should i see a doctor if my period came on 2 times. in the same month ?

Not necessarily: Since most women have menstrual cycles that are less than 30 days in length and most months are 30 or 31 days, it is common to occasionally have a period at the very start of the month and another at the end of that month. The better way to know if something is a problem is to count the days from the start of one period to the start of the next. Normal is 21-35 days ( or 42 days by some sources).

Vaginal bleeding: This probably wasn't a second menstrual period, but some other cause of bleeding between periods. Any abnormal vaginal bleeding should be professionally evaluated. There are many possible causes, often minor (hormonal issues, breakthrough bleeding, etc) but sometimes serious (infection, fibroid tumor, etc). See your gyn or PCP. Depending on age and sexual lifestyle, you may need STD testing.