Can a vital tooth nerve/pulp be infected? have pulpitis but not sure if will get better or not.

Too Early to Tell: An increase in sensitivity of the nerve of a tooth that can have many causes. If you have a deep cavity in that tooth it is probably the cause. Get it fixed right away before you need a root canal. If the dentist can't find a cavity, you may be grinding or clenching on the tooth at night., or have suffered a blow - say from a fall. If there's no infection and you remove the cause it'll heal.

Pulpitis: Pulpitis merely denotes an inflammation of the tooth pulp. It can be reversible and go away or irreversible and lead to a degradation of the tissues of the pulp canal and becoming infected. Your own dentist is the best one to determine cause, treatment, and likelihood of you requiring treatment such as Root Canal Therapy. We can't always predict that especially over the internet.

If vital, no: Once the tooth is infected, it becomes non vital.