You are exactly right. You have 'Neurogenic Thoracic outlet syndrome(n TOS)". From your description of symptoms you have the following factors in favour of the diagnosis of TOS.
1. You do typing work- that very important job related risk factor.
2.You have been told by somebody to have extra ribs.
3.You have had trauma in neck and shoulder previously- which brings to notice or agravates the symptoms of cervical ribs.
4.You have numbness
and feeling of cold
in both sides of your hands.
5.You have headache frequently.
All of the above go in favour of neurogenic Thoracic Outlet Syndrome.
Now for confirm diagnosis ,you need to get a cervical spine
Xray and CT/MRI
scan if needed later on.
A few clinical tests also can help in diagnosis. Best would be to consult your vascular specialist .
In case of a confirmed TOS, you will be benefited by Physiotherapy
. Arround 70-80 % of patients do well with a 6 month physiotherapy training.
And only in case of failure of physiotherapy trial , you may need surgical decompression of TOS,that is excision of the extra(Cervical rib) rib and neurolysis for brachia plexus.
Hope you are satisfied with answer.
Dr Srujal Shah