Vagina feels like it has a rash, almost like a diaper rash. Can it be the same thing?

Yes. There are several things that can cause a problem like this, including irritation, allergic reaction, yeast or bacterial infection, psoriasis, seborrheic dermatitis, and others.
Maybe. There are various etiologies for diaper rash, vaginitis (infection/irritation within the vagina), and vulvitis (infection/irritation externally). The most common are yeast, bacteria, stds and contact dermatitis. Treatment depends upon the source of the irritation; your doctor can determine what's the best way to treat you.