The quick answer to your question is yes, premature babies can, and often get infant respiratory distress syndrome. The reason for this stems from the fact that certain steps of lung maturity occur between the 33rd and 37th week of pregnancy. When a women at 33 weeks (such as yourself) comes in to the hospital in labor, the first step is to see if the labor can be delayed. This is done with medications that slow down the contractions. If labor cannot be slowed or stopped, then a steroid medication is given to the mother which can accelerate the maturity of the baby's lungs.
After birth, the baby is taken to the neonatal intensive care unit and an assessment of the baby's lungs is made. Some baby's require a machine to help them breath until they are able to breath on their own. Since your baby was already born, then he or she either has infant respiratory distress syndrome, or doesn't. In other words it if your baby didn't have problems right away, you are probably in the clear. There are other risks to prematurity, but most studies that have examined other issues have looked at babies born before 33 weeks.
If your baby is home now, then I would suggest that you schedule an appointment with the pediatrician
. He or she will be able to discuss all the important information you need to know about premature births.