My understanding of Honda main relays are that they normally fail when the car or interior is hot, with a no-start being the symptom. Usually when allowed to cool, it'll start right up, and I'm not aware of poor running being a main relay issue. You can take it out very easily and ohm it out with a multimeter.
When my coil failed, it ran fine with little throttle, but stumbled badly when the gas pedal was pressed, so that doesn't sound like your issue either. (I went to the auto parts store and they let me compare it with a new one.)
The high revving might just be because you have to keep your foot in it to accelerate, so it's upshifting later.
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