If your consultant physician has asked for a CT, then there is probably need for one. Also, he/she would have analysed the risks/rewards ratio.
CT is better in diagnosing bone related issues, in addition to soft tissue problems, than an MRI.
Although it is true that multiple exposure to medical radiation (including CT) can slightly increase the chance of developing Cancers, the risk is very slight, and most often almost nil.
As far as Contrast is concerned, it is safe to use unless you have a known allergic history or are a
kidney/
liver/cardiac patient.
Next Steps
In short, consult a well experienced clinician and if he suggests another CT/MRI with contrast, be assured that he have analysed the benefits to outweigh risks. Just go for it.
Health Tips
Get well soon.