@anon167994: It would depend on what they were imaging and how they were going about it.
We always try to limit exposure to patients as much as possible, however CT scans are also incredibly valuable for diagnosing illness and staging disease.
Feeling sick and vomiting after a scan would most likely be caused by a minor reaction to any contrast used during the procedure. It could also simply be stress as having an exam can indeed be quite stressful.
If you are at all concerned, there is nothing wrong with talking to your doctors about it. Ask them why they need to perform another CT and if there are any exams they could do that would not involved ionizing radiation (such as an MRI or ultrasound). Depending on what they are looking for, this may or may not be possible.
As for actual damage caused by the CT, talk to the radiologist if possible, and they should be able to explain possible problems that could occur from exposure to radiation. The less radiation you are exposed to, the better. That being said, odds are very very low that four scans could lead to any long term problems.
Talk to your doctor. It is their job to make sure you understand the examination and to answer any questions or concerns you have regarding it.