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

GI doc. Vomiting blood may be a serious issue, reflecting e.g. Ulcer of stomach or duodenum, lacerated blood vessel, varicose veins of esophagus or stomach, inflammation of stomach or gut. May be self-limited, or not. Should see gastroenterologist, for further evaluation (endoscopy), or endoscopic rx is needed. Can work with your primary doc.