I suspect that you have cut the nerve that supplies sensation to the fingertip when you cut your finger. This may or may not heal. Peripheral nerves do regenerate but it can take a long time (months or even years).
I would recommend you see your doctor just to have a full evaluation and make sure nothing else is going on.
Advice and opinions given are based on the information provided and must not be considered an official medical recommendation. The limitations of the internet prevent an appropriate evaluation. Always consult your doctor if there is concern.