If i were you

1. I would check with couple of other pyhisicians. I'm not sure where you are. if you are in US, you can always see after-hour clinic drs by numorous reasons. That's my easy trick to get another point of view without too much hectics.
2. If dr really suggests to do CT, i would follow what dr says. Here in US, dr doesn't give out those tests that easily. I almost urged my son's dr to give him a CBC after he was in high fever for a week.
Totally understand your feeling and God bless you.