Can my stomach flu go away on its own, or do I need to get meds from a doctor?

Maybe. Depends on age, severity, and underlying medical problems, but usually is self-limiting illness.
G.i. FLU 'Goes AWAY' Viral gastroenteritis ('stomach flu') is usually self limiting and requires no treatment but sometimes anti-nausea prescription meds (e.g. Phenergan) may be helpful. You have to get seen to get a prescription, however. If diarrhea lasts > 1 week you may have a infectious diarrhea requiring stool tests and possible anti-biotics. Hope you are better soon!