I suffer the same problem. I've always had really bad sinus problems and typically breath through my mouth. When I record backing vox, I'm constantly editing out breaths. But that's not applicable if breathing is getting picked up over the primary instrument.
Instead of EQ'ing, you could try some different mic techniques?
If the guitar part is loud, you could move the mic back and play even louder.
Have you tried changing the polar pattern (I think Rode NT2a has omni/cardio/figure 8)? Depending on how much rejection the cardio/figure 8 has, you might even try moving the mic closer to you, a bit above the guitar but pointing down towards the guitar, so that your breath is directed outside the pickup pattern.