My shoulders remain cold specially in d night..now this chills has reached my elbows, palms, feet....hand and body tremors when anxious?

Get checked: You should be checked out to see if you have a neurological problem giving you this sensation of "chills." following up on your thank-you note, the list of causes of peripheral and central neuropathies is too extensive to allow enough detail here. It may not even turn out to be a neurological problem!

See a doctor: Need more info, and you need to provide a full history and submit to a physical exam before this can be successfully worked out. Go and see a pcp.