Although I agree with doctors being, very often, uncaring, in this case your doctor is right. A CT scan wouldn't tell him any more than he already knows and it would expose you to radiation unnecessarily.
I know exactly how you feel, I think your dr should do the test, you are young and need to know the things that can help or hurt you, so that you may have to best quality of life. I hope you can get some help soon, worrying can only make things worse! Let us know how things work out for you. GOD BLESS