Is it normal to have your period two different times in one month?

No that isn't normal. You need to see your doctor to rule out pregnancy and other problems.However, It depends on when you had it and how long the month is. For example, If you have the first one during the first week of the month and it was a month that had 30 or 31 days, it is possible for your period to start in the last days of the month. However, if they came like a week or two weeks apart, then by all means see your doctor.