Thanks for posting your query,
It is very unlikely that your symptoms especially as they present are related to depo shots especially after all these while on it without any problems.
If you are feeling nauseated and have cold extremities, then there is an obvious underlying diseases condition that needs to be investigated and seems those symptoms are unspecific, this will require that your doctor examine you carefully and run a series of blood tests including hormone tests (thyroid, reproductive hormones etc). Your doctor should screen for pregnancy
(yes possible even on depo shots) and if negative should send you to an internist for further review. Cold extremities could be caused by poor circulation (if so, then the cause should be identified immediately), peripheral neuropathy
(cause such as diabetes
should be checked), vitamin B12 deficiency
(supplements could be given and if improvement then, the cause is that), autoimmune diseases etc.
An internist could determine the cause and effectuate a treatment.
Also important is to consider the fact that your problem could be psychological.
Hope this helps