I am receiving a civil service pension from usps and I am becoming unable to use my hands often due to severe carpal tunnel issues for past 6-7 years. Am I able to apply for SS disability?
You can always apply for Social Security benefits, but I can't tell you whether or not you'd qualify without additional information. Social Security disability (SSDI) benefits can only be paid for months prior to when a person reaches full retirement age (FRA), so whether or not you could qualify depends in part on your age. SSDI benefits convert to regular Social Security retirement benefits when a person reaches FRA.
Also, in order to potentially qualify for SSDI benefits a person must meet an insured status requirement. In order for a person older than age 31 to be insured for SSDI, they must have at least 20 quarters of Social Security coverage within the 40 quarter period leading up to the time they became disabled. So, in other words, you would basically need to have worked and paid into Social Security for the equivalent of at least 5 years within the 10 year period leading up to when your disability began (https://www.ssa.gov/planners/disability/qualify.html#anchor1).