Yes. Pulpitis or inflammation of the nerve inside the tooth can be quite painful. When it is acute and severe the tooth will probably require endondontic therapy or root canal to resolve the problem.
Yes. Pulpitis pain can have a range of presentations. If you are experiencing severe acute pain it could very well be a pulpitis, but it could also be periodontal/gum pain, muscular pain, or any number of other things. See your dentist to help determine the problem!