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10 years is quite a long time. It is highly unlikely that you can get rabies by an exposure 10 years back. Usually with infection of rabies virus, (through a bite of rabid animal) shows symptoms in 20 to 90 days. The period can be as long as more than a year. But I have not come across a period more than that.
Regarding immunization, rabies is one of the few diseases for which post-exposure prophylaxis is available. It is always preferred to get yourself immunized along with anti-rabies serum.