It's too early for you to take a pregnancy if your last period began on March 7th.
According to a typical cycle, you'll want to hold off on testing until the first week of April.
The symptoms you're describing, especially pain on just one side of your lower stomach, along with the date of your last period is indicative of ovulation.
Ovulation happens roughly two weeks before the start of our next period. When ovulation occurs an egg is released from on of the Fallopian tubes and this happens at random which is why this month you feel it on your right side and next month you might feel it on the left side.
Experiencing pain and sickness during ovulation is called "mittelschmerz" which means "middle pain" in German.