There are many reasons your back might be hurting after a Romanian deadlift. This can include poor technique, such as insufficient core bracing, a rounded back, not keeping the bar over your mid-foot, or not correctly hinging at the hips. Another reason could be that you're going too hard too soon. In that case, maybe lower the weight or volume of your training. Of course, regular muscle soreness from exercise is to be expected; however, if you're experiencing severe discomfort or it doesn't go away, you might need to visit your doctor.