Ohhhh, yes. Wheat (and other gluten grains) can most certainly have this effect!
I see what you're saying about not being sure you want to make the sacrifice permanently, but read up on what grains do to your intestines (think cumulative damage that can lead to infections, cancer, etc., not just temporary discomfort) and you might find that your perspective changes.
I wonder if something like pizza is easier to stomach because the fat buffers the gluten's impact? No idea whether that's true. Just a thought on why the wheat seems to disturb you more sometimes than others.