Are any special tests needed, or can a regular doctor see me for my peptic ulcer?

Yes: An appropriately trained internal medicine doctor can cure this.

Follow-up of ulcer: Once your ulcer is objectively documented, treatment for it may involve prescriptions of acid blocker drugs, & as appropriate anti-helicobacter medication. Your internist can certainly prescribe these agents, as well as advise you regarding nsaid's & Aspirin so as to promote faster healing of the ulcer. However, biopsy & recheck of a stomach ulcer requires endoscopy from your gastroenterologist.