It is not surprising that the lithium carbonate (Eskalith – Carbolith, in Canada) is causing parkinsonian symptoms. In order to counteract the manic stages, this medication often causes opposite reactions.

Some of the PD-like symptoms include muscle weakness, drowsiness, lack of coordination, tremor twitching, urinary frequency, dystonia, blurred vision, nystagmus, slowed cognitive function, cogwheel rigidity, sexual dysfunction among others.

Because you have been taking lithium carbonate for several years, you should discuss this with your doctor. You can request that your serum lithium concentration levels be checked, The symptoms usually occur at the higher concentrations although tremor has been known to occur at lower levels.

http://www.bipolarworld.net/Medications/Mood%20Stabilizers/meds6.htm

I just found this abstract (hope the link works) which you should probably read – it isn’t complete but it does support getting tested.
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B8CWJ-4KWCS4T-7&_user=10&_origUdi=B6T70-47VXBRY-F&_fmt=high&_coverDate=12%2F31%2F1998&_rdoc=1&_orig=article&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=769508b85ea0ef7a7cff085c08750a37

It could be that you will need to reduce your dosage although in some cases stopping the medication (for a while at least) is recommended.

As a matter of fact, if the lithium carbonate is not causing the symptoms, it will be much easier for a neurologist to begin diagnosing the problem. You might want to keep a journal of the exact symptoms, when they occur for discussion with your doctor.

Best wishes