There is no rainy season as such in the Dominican Republic, if by rainy season you mean monsoon like conditions.
However, some months are statistically more wet than others, depending on where you are. Around Puerto Plata November through January are wet months, and Puerto Plata based on a yearly average gets more rain than Punta Cana.
The wettest months around Punta Cana are the months of summer.
But notice that even during a wet period you will usually get sunny intervals. And temperatures tend to be pleasant anyway. In March it should gradually get even warmer and sunnier. No guarantees, though. The climate in the DR is maritime which means that it is unpredictable. And it isn't likely that you will avoid rain altogether on your holiday. It will usually be a heavy, but short shower. Rain is what makes the North of the island so extremely green, so enjoy it. You will bring home a nice tan in spite of it.
Regards,
Susanne
