I understand your concern regarding the tests for HIV as this dreadful disease has caused quite a scare. Thats why WHO has come up with very strict guidelines to avoid missing HIV positive cases.
However, as your query suggests that you have had a low risk exposure on your finger.
Ideally you should have washed the wound immediately and post exposure prophylaxis should be started within two hours of exposure.
There are many tests available for detection of HIV.
They can be grouped as rapid tests, supplemental tests and confirmatory tests.
As your doctor has suggested you have undergone HIV PCR which is a confirmatory test. The rapid tests help in screening as well as diagnosis.
Your doctor is right that as all the tests came negative, You do not have to worry much.
However, according to guidelines, HIV test
is performed at 6 weeks, 12 weeks and 6 months post exposure, regardless of whether or not Post Exposure Prophylaxis was taken or not.
Please consult your doctor for the test to be done and confirmatory tests are preferred.