Which type of specialist can test me for small cell lung cancer (the types of lung malignancy that cannot be seen on xray)?

Pulmonologist: I think you may be misinformed. You do not have lung cancer. But, testing is best done in this situation with a pulmonologist.

Pulmonary: If you have some cause or reason, symptoms that would in any way cause concern for a possible lung cancer, than a lung specialist (pulmonary dr.) would be able to diagnose a you accordingly, which may include a history and physical examination, possible testing including labs, x-rays, and possible diagnostic bronchoscopy.