CT scan with contrast show nerves? Mri?

I have lower jaw pain under ear and neck for 8 months now. Went to dentist,oral surgeon, physician, endodontist,tmj specialist, neurologist. Taken multiple xray at dentist office.Been to 5 dentist office and taken dental x-rays there since June. Had 3 dental CBCT scan so far.One dental CBCT taken for a tooth in June, another Dental CBCT taken for TMJ in Sept, last dental CBCT taken 2 weeks back for a tooth. No proper diagnosis yet.My physician want me to take CT scan of neck soft tissue with contrast to check my lower jaw and neck pain.I have tenderness, burning,sore pain. Have some lump spots which hurts to touch and looks mildly swollen. I went to a neurologist to check if it's neuralgia or nerve issue. Neuro ordered MRI brain with contrast.he didn't include MRI neck.My GP want me to take CT neck scan soft tissue with contrast.He said,if I do CT neck scan,no need of MRI imaging.So,he want me to do CT neck scan.Does CT with contrast neck soft tissue show the nerves or I should do MRI?