Can I have a baby normal after a c section?

Yes, but concerns. Vaginal birth after c section = vbac, is often medically possible. After a c-section, the uterus has a scar from healing, that is the major concern. Even though the scar may not look bad before the uterus stretches, as your uterus expands for the growing fetus, the scarred area may become thin, with higher risk of tearing during contractions. Some hospitals decide that the legal risks are too high.
What is normal? When almost 40% of us babies are born via c-section, one has to wonder what is normal delivery nowadays. I presume you are asking about vbac (vaginal birth after cesarean); that is a viable option for women with one prior lower uterine transverse scar of normal weight for height and desirous of at least two more pregnancies after their c-section. Risks with vbac are mostly fetal - dicsuss with md!