Is this a mild case of stomach flu if diarrhea and no vomiting?

What is flu? Impossible to tell what your diarrhea is due to, but it may well be viral. It is doubtful that it is due to the influenza virus without other symptoms. The term "flu" is often misused by non-physicians and this leads to a great deal of confusion.
Could be. Hard to say but very well may be. Stay well hydrated and see a doctor if not better in 5-7 days.

Related Questions

I had the stomach flu for 18 recently...started out after a plane ride feeling a little tired, then mild diarrhea, then occasional vomiting. Normal?

Sounds normal. That sounds normal for a viral GI infection. What do you mean by 18 though? A viral infection can last a little longer than a few days so don't be alarmed by this. Read more...